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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Representation; uniform symmetric functions; simultaneous roots; algebraic equations; sum of products of determinants; coefficients; recurrent; function of lower order Equations in general fields, Polynomials in real and complex fields: location of zeros (algebraic theorems), Algebraic functions and function fields in algebraic geometry, Determinants, permanents, traces, other special matrix functions, Ordinary representations and characters, Classification of real functions; Baire classification of sets and functions, Symmetric functions and generalizations On representing the uniform symmetric functions of the simultaneous roots of two algebraic equations. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic number fields; algebraic function fields; algebraic \(p\)-adic height pairing; elliptic curve; Selmer group; complex multiplication; pairing of Galois cohomology groups; Poincaré group; Galois extension Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On a Galois extension with restricted ramification related to the Selmer group of an elliptic curve with complex multiplication | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Artin-Schreier extensions of function fields; automorphisms; \(k\)-error linear complexity; joint linear complexity; multisequences Cryptography, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Shift register sequences and sequences over finite alphabets in information and communication theory Multisequences with large linear and \(k\)-error linear complexity from a tower of Artin-Schreier extensions of function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press \(\zeta (s)\) and \(L(s, \chi)\), Research exposition (monographs, survey articles) pertaining to number theory, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Distribution of primes An introduction to the theory of the Riemann zeta-function. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces minors of multidimensional matrix; Cohen-Macaulay; Koszul algebra; Segre embedding; decomposable tensor; Hilbert function; Gröbner basis; catalecticant; ample divisor; defining ideal of blowup H.T. Hà, Box-shaped matrices and the defining ideal of certain blowup surfaces , J. Pure Appl. Alg. 167 (2001), 203-224. Linkage, complete intersections and determinantal ideals, Embeddings in algebraic geometry, Special surfaces, Determinants, permanents, traces, other special matrix functions Box-shaped matrices and the defining ideal of certain blowup surfaces. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(KP\)-equation; KdV equation; Whitham equations; completely integrable partial differential equations; abelian functions of algebraic curves; Riemann surfaces; Baker-Akhiezer function DOI: 10.1080/00036819708840541 Algebraic functions and function fields in algebraic geometry, Differentials on Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Jacobians, Prym varieties, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) The Whitham equations revisited | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic curves over global fields; arithmetic function fields; sheaves of differentials; Kähler differentials; arithmetic schemes; valuation rings Kunz, E.; Waldi, R.: Integral differentials of elliptic function fields. Abh. math. Sem. univ. Hamburg 74, 243-252 (2004) Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry, Valuation rings Integral differentials of elliptic function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces pre-spectral data for commutative subalgebras of rank 1; algebras of differential operators; Godeaux surfaces Surfaces of general type, Divisors, linear systems, invertible sheaves, Derivations and commutative rings On divisors of small canonical degree on Godeaux surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces isomorphism of Witt rings; Witt equivalence of fields; global field; algebraic function field Koprowski, Przemysław, Local-global principle for Witt equivalence of function fields over global fields, Colloq. Math., 91, 2, 293-302, (2002) Algebraic theory of quadratic forms; Witt groups and rings, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Quadratic forms over general fields, Algebraic functions and function fields in algebraic geometry Local-global principle for Witt equivalence of function fields over global fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces twin irreducible polynomials; parity barrier over function fields; short character sums; level of distribution for irreducible polynomials Étale and other Grothendieck topologies and (co)homologies, Arithmetic theory of algebraic function fields, Polynomials over finite fields, Goldbach-type theorems; other additive questions involving primes, Primes in congruence classes On the Chowla and twin primes conjectures over \(\mathbb{F}_q[T]\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces inverse Galois theory; Galois coverings; rigid analytic spaces; Galois extensions of function fields Inverse Galois theory, Coverings in algebraic geometry Rigid geometry and Galois extensions of function fields in one variable | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces rational curve; formally real field; space of orderings; dense orbits property; \(Q_ 1\)-fields; function fields of real algebraic varieties; elliptic curve Real algebraic and real-analytic geometry, Ordered fields, Arithmetic ground fields for curves, Special algebraic curves and curves of low genus, Rational and unirational varieties, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) A characterization of rational and elliptic real algebraic curves in terms of their space of orderings | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces quasi-symmetric algebra; symmetric algebra; Rees algebra; associated graded ring; module of derivations; module of tangent vector fields; algebraic hypersurface Derivations and commutative rings, Syzygies, resolutions, complexes and commutative rings, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Other special types of modules and ideals in commutative rings, Torsion modules and ideals in commutative rings, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Dynamical aspects of holomorphic foliations and vector fields, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Homological methods in commutative ring theory, Theory of modules and ideals in commutative rings, Commutative rings and modules of finite generation or presentation; number of generators, Dimension theory, depth, related commutative rings (catenary, etc.), Low codimension problems in algebraic geometry On Aluffi's problem and blowup algebras of certain modules | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Towers of function fields; congruence function fields; genus; rational places; limits of towers; Zink's bound; cubic finite fields; Artin--Schreier extensions; Drinfeld--Vlăduţ bound; Hasse--Weil bound [4]A. Bassa, A. Garcia and H. Stichtenoth, A new tower over cubic finite fields, Moscow Math. J. 8 (2008), 401--418. Arithmetic theory of algebraic function fields, Curves over finite and local fields, Modular and Shimura varieties, Rational points A new tower over cubic finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic function fields; algebraic curves; Riemann-Roch theorem; coding theory; algebraic-geometry codes; differentials; towers of functions fields; Tsfasman-Vladut-Zink theorem; trace codes Stichtenoth, H., \textit{Algebraic Function Fields and Codes}, 254, (2009), Springer, Berlin Algebraic functions and function fields in algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects) Algebraic function fields and codes | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces affine schemes; categories of quasicoherent sheaves; Serre's theorem; noncommutative localizations; structure sheaves; schematic algebras; noncommutative algebraic geometry; graded algebras; Ore sets; quantum groups; braided categories F. van Oystaeyen. \textit{Algebraic geometry for associative algebras}. Series ''Lect. Notes in Pure and Appl. Mathem.'' \textbf{232} (Marcel Dekker: New York, 2000). Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Research exposition (monographs, survey articles) pertaining to associative rings and algebras, Associative rings of functions, subdirect products, sheaves of rings, Graded rings and modules (associative rings and algebras), Ore rings, multiplicative sets, Ore localization Algebraic geometry for associative algebras | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Frobenius algebras; Rosenberg-Zelinsky sequence; Morita equivalences; Picard groups; categories of bimodules; monoidal categories; algebra automorphisms; exact sequences Barmeier, T.; Fuchs, J.; Runkel, I.; Schweigert, C.: On the rosenberg-zelinsky sequence in abelian monoidal categories, J. reine angew. Math. 642, 1-36 (2010) Module categories in associative algebras, Picard groups, Bimodules in associative algebras, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Two-dimensional field theories, conformal field theories, etc. in quantum mechanics On the Rosenberg-Zelinsky sequence in Abelian monoidal categories. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces surfaces of general type; canonical surfaces; canonical ring; Gorenstein algebras; canonical projections Böhning, C., Canonical surfaces \(\mathbb{P}^4\) with \(p_g = p_a = 5\) and \(K^2 = 11\), Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 18, 39-57, (2007) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Syzygies, resolutions, complexes and commutative rings, Divisors, linear systems, invertible sheaves, Surfaces of general type Canonical surfaces in \(\mathbb P^4\) with \(p_g=p_a=5\) and \(K^2=11\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces compatible systems of Galois representations; independence of algebraic monodromy groups; automorphic compatible systems; compatible systems over global function fields Galois representations, Representation-theoretic methods; automorphic representations over local and global fields, Langlands-Weil conjectures, nonabelian class field theory, Structure of families (Picard-Lefschetz, monodromy, etc.), Positive characteristic ground fields in algebraic geometry Independence of algebraic monodromy groups in compatible systems | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Polyakov string; zeta-function regularization; moduli of Riemann surfaces; Quillen metric; determinant bundle Bost, J. B.: Fibrés déterminants, déterminants régularisés et mesures sur LES espaces de modules des courbes complexes. Astérisque 152-153, 113 (1987) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Families, moduli of curves (algebraic), Riemann surfaces, Quantum field theory; related classical field theories Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes. (Determinant fiber bundles, regularized determinants and measures on moduli spaces of complex curves.) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Noncommutative symmetric systems; noncommutative symmetric functions, Azumaya algebras Zhao, W.: Noncommutative symmetric systems over associative algebras. J. pure appl. Algebra 210, No. 2, 363-382 (2007) Symmetric functions and generalizations, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms and endomorphisms, Algebraic aspects of posets Noncommutative symmetric systems over associative algebras | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces dimension of linear systems of curves; Hilbert polynomial; generic Hilbert function; rational surfaces; zero-cycles B. Harbourne, \textit{The geometry of rational surfaces and Hilbert functions of points in the} \textit{plane}, in: Proceedings of the 1984 Vancouver Conference in Algebraic Geometry, CMS Conf. Proc. 6, Amer. Math. Soc., Providence, RI, 1986, 95--111. [30] B. Harbourne, \textit{Free resolutions of fat point ideals on }P2, J. Pure Appl. Algebra 125 (1998), 213--234. Divisors, linear systems, invertible sheaves, Algebraic cycles, Rational and unirational varieties The geometry of rational surfaces and Hilbert functions of points in the plane | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces skew-symmetric matrix; globally generated vector bundle; constant rank of matrices of polynomials Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic systems of matrices Planes of matrices of constant rank and globally generated vector bundles | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Krichever-Novikov algebras; meromorphic vector fields; higher genus Riemann surfaces M. Schlichenmaier, ''Krichever-Novikov Algebras for More Than Two Points,'' Lett. Math. Phys. 19, 151--165 (1990). Differentials on Riemann surfaces, Curves in algebraic geometry, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Krichever-Novikov algebras for more than two points | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces multitoric surfaces; determinantal surfaces; Euler obstruction of a function; Brasselet number Local complex singularities, Obstruction theory in algebraic topology, Toric varieties, Newton polyhedra, Okounkov bodies Multitoric surfaces and Euler obstruction of a function | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces curves over number fields; diophantine equations; symmetric power of algebraic curves; Mordell conjecture; Jacobian variety; geometric gap principle; arithmetic gap priciple; gap principle for abelian varieties; quadratic point Joseph H. Silverman, Rational points on symmetric products of a curve, Amer. J. Math. 113 (1991), no. 3, 471 -- 508. Rational points, Arithmetic ground fields for abelian varieties, Arithmetic ground fields for curves, Higher degree equations; Fermat's equation Rational points on symmetric products of a curve | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Cayley-Bacharach theorem; complete intersections; Hilbert function of graded Gorenstein algebras Davis, Gorenstein algebras and the Cayley-Bacharach theorem, Proc. Amer. Math. Soc. 93 pp 593-- (1985) Complete intersections, Projective techniques in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Homological methods in commutative ring theory Gorenstein algebras and the Cayley-Bacharach theorem | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces monomialization; field extension of two-dimensional function fields Cutkosky, S.D., Piltant, O.: Monomial resolutions of morphisms of algebraic surfaces. Special issue in honor of Robin Hartshorne. Commun. Algebra 28, 5935--5959 (2000) Rational and birational maps, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry Monomial resolutions of morphisms of algebraic surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces curves defined over a valuation ring; function field; first order language of valued fields; stable reduction theorem [GMP] B. W. Green, M. Matignon and F. Pop,On valued function fields III, Reductions of algebraic curves, Journal für die Reine und Angewandte Mathematik432 (1992), 117--133. Arithmetic ground fields for curves, Valued fields, First-order arithmetic and fragments On valued function fields. III: Reductions of algebraic curves. Appendix (by Ernst Kani): The stable reduction theorem via moduli theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces division algebras; Brauer groups; degrees; indices; \(p\)-adic curves; algebraic function fields Eric Brussel, On Saltman's \?-adic curves papers, Quadratic forms, linear algebraic groups, and cohomology, Dev. Math., vol. 18, Springer, New York, 2010, pp. 13 -- 39. Finite-dimensional division rings, Ramification and extension theory, Brauer groups of schemes, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Brauer groups (algebraic aspects) On Saltman's \(p\)-adic curves papers. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces covering spaces of projective manifolds; ample line bundle; holomorphic functions of slow growth; Riemann surfaces with corona; generating Hörmander algebras on covering spaces; dichotomy; covering group; harmonic functions; weighted Bergman spaces Finnur Lárusson, Holomorphic functions of slow growth on nested covering spaces of compact manifolds, Canad. J. Math. 52 (2000), no. 5, 982 -- 998. Holomorphic functions of several complex variables, Coverings in algebraic geometry, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Riemann surfaces, Continuation of analytic objects in several complex variables Holomorphic functions of slow growth on nested covering spaces of compact manifolds | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces graded Clifford algebras; skew Clifford algebras; twists of Clifford algebras; regular algebras; quadric systems; quadratic algebras Nafari, M.; Vancliff, M., Graded skew Clifford algebras that are twists of graded Clifford algebras, Communications in Algebra, 43, 719-725, (2015) Rings arising from noncommutative algebraic geometry, Quadratic and Koszul algebras, Ordinary and skew polynomial rings and semigroup rings, Clifford algebras, spinors, Noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras) Graded skew Clifford algebras that are twists of graded Clifford algebras. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(K_ 2\) of fields; Brauer group; cyclic algebras; generators Merkurjev, A. S.: On the structure of the Brauer group of fields. Math. USSR izv. 27, No. 1, 141-157 (1986) Galois cohomology, \(K\)-theory of global fields, Brauer groups of schemes, Skew fields, division rings, \(K_2\) and the Brauer group On the structure of the Brauer group of fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Brauer groups of fields; elements of exponent p; classes of cyclic algebras of degree p A. S. Merkurjev, Brauer groups of fields, Comm. Algebra 11 (1983), 2611--2624. Brauer groups of schemes, Galois cohomology Brauer groups of fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces rational surfaces; ruled surfaces; Néron-Severi group; blowing-up; Picard number of an algebraic surface Rational and ruled surfaces, Divisors, linear systems, invertible sheaves Fixed loci of the anticanonical complete linear systems of anticanonical rational surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces valued function fields; existence of regular functions; Henselian constant field; divisor reduction map; divisor group; elementary class Green, B.; Matignon, M.; Pop, F.: On valued function fields II: Regular functions and elements with the uniqueness property. J. reine angew. Math. 412, 128-149 (1990) Valued fields, Algebraic functions and function fields in algebraic geometry, Model theory of fields, Arithmetic theory of algebraic function fields, Field extensions On valued function fields. II: Regular functions and elements with the uniqueness property | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Brauer group of function field; reciprocity sequence; higher-dimensional function fields; smooth projective varieties; threefolds J. -L. Colliot-Thélène, ''On the reciprocity sequence in the higher class field theory of function fields,'' in Algebraic \(K\)-Theory and Algebraic Topology, Dordrecht: Kluwer Acad. Publ., 1993, vol. 407, pp. 35-55. Generalized class field theory (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic theory of algebraic function fields, Geometric class field theory, Étale and other Grothendieck topologies and (co)homologies On the reciprocity sequence in the higher class field theory of function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hilbert modular function for \(\sqrt{5}\); periods of \(K3\) surfaces; period differential equations; theta constants Nagano, A, A theta expression of the Hilbert modular functions for \(\sqrt{5}\) via period of K3 surfaces, Kyoto J. Math., 53, 815-843, (2013) \(K3\) surfaces and Enriques surfaces, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Classical hypergeometric functions, \({}_2F_1\) A theta expression of the Hilbert modular functions for \(\sqrt{5}\) via the periods of \(K3\) surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces affine variety minus bound on the height of integral points; hyperplanes in general position; number of integral points; function fields Wang, J.T.-Y., \textit{S}-integral points of \(\mathbb{P}^n - \{2 n + 1 \text{ hyperplanes in general position} \}\) over number fields and function fields, Trans. amer. math. soc., 348, 3379-3389, (1996) Arithmetic theory of algebraic function fields, Rational points, Varieties over global fields \(S\)-integral points of \(\mathbb{P}^ n- \{2n+1\) hyperplanes in general position\(\}\) over number fields and function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces theory of invariants; algebra of invariants; algebra of symmetric polynomials; Cohen-Macaulay rings; Gorenstein rings; groups generated by pseudoreflections; polynomial algebras L.~Smith. \textit{Polynomial invariants of finite groups}, volume~6 of \textit{Research Notes in Mathematics}. A K Peters Ltd., Wellesley, MA, 1995. Ordinary representations and characters, Exact enumeration problems, generating functions, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Families, moduli of curves (algebraic), Vector and tensor algebra, theory of invariants, Reflection groups, reflection geometries Invariants of finite groups and their applications to combinatorics | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces real function fields; real holomorphy ring; valuation rings; formally real residue field; regular projective model; rational point; real prime divisors; signatures of higher level; sums of n-th powers; local-global principle; weak isotropy; quadratic forms; Henselizations Schülting, H. W.: The binary class group of the real holomorphy ring. (1986) Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings Sums of 2n-th powers in real function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cyclic trigonal Riemann surfaces; vanishings of the associated theta function; Jacobian; hyperelliptic theta functions R.D.M. Accola, \textit{On cyclic trigonal Riemann surfaces}, Trans. Amer. Math. Soc. 283 (1984) 2, 423--449. Coverings of curves, fundamental group, Compact Riemann surfaces and uniformization, Theta functions and abelian varieties, Special algebraic curves and curves of low genus, Families, moduli of curves (analytic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) On cyclic trigonal Riemann surfaces. I | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces infinite tower of function fields; asymptotically good tower; long algebraic-geometric codes with good parameters; Artin-Schreier extensions; Kummer extensions Garcia, A.; Stichtenoth, H., Asymptotically good towers of function fields over finite fields, C. R. Acad. Sci. Paris Sér. I Math., 322, 11, 1067-1070, (1996) Curves over finite and local fields, Arithmetic ground fields for curves, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory Asymptotically good towers of function fields over finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces function fields of conics; Zariski problem; transcendental extension; rationality; regular function field; Amitsur-MacRae theorem Jack Ohm, Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 333 -- 363. Transcendental field extensions, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces bibliography; orthogonal reflections; regular polyhedra; Gosset; polyhedra; survey; basic invariants of reflection groups; diameter theory of algebraic surfaces; skew reflections V. F. Ignatenko, ''Some problems in the geometrical theory the invariants of groups generated by orthogonal and oblique reflections'', In:Problemy Geometrii, Vol. 16, Itogi Nauki i Tekhn., All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1984), pp. 195--229. Reflection groups, reflection geometries, Polyhedra and polytopes; regular figures, division of spaces, Geometric invariant theory, Group actions on varieties or schemes (quotients), Other algebraic groups (geometric aspects), Other geometric groups, including crystallographic groups, Orthogonal and unitary groups in metric geometry Some questions in the geometric theory of invariants of groups generated by orthogonal and oblique reflections | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Anderson-Thakur function; \(L\)-functions in positive characteristic; function fields of positive characteristic Bruno Anglès & Federico Pellarin , Functional identities for \(L\) -series values in positive characteristic , J. Number Theory 142 (2014), p. 223-251 Zeta and \(L\)-functions in characteristic \(p\), Modular forms associated to Drinfel'd modules, Formal groups, \(p\)-divisible groups Functional identities for \(L\)-series values in positive characteristic | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces biholomorphic classification of ruled non-rational smooth complex projective surfaces; hyperplane section Livorni, E. L., \textit{classification of algebraic surfaces with sectional genus less than or equal six. III: ruled surfaces with dim} {\(\phi\)}\_{}\{kx\(###\)L\}, Math. Scand., 59, 9-29, (1986) Moduli, classification: analytic theory; relations with modular forms, Families, moduli, classification: algebraic theory, Rational and ruled surfaces Classification of algebraic surfaces with sectional genus less than or equal to six. III. Ruled surfaces with \(\dim \phi_{K_ X\otimes L}(X)=2\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces formal languages; algebraic geometry over finite fields; rationality of zeta function; zeta function; formal power series; cyclic language; minimal ideals in finite semigroups; characteristic series; cyclic recognizable language; traces of finite deterministic automata; sofic system; symbolic dynamics J. BERSTEL and C. REUTENAUER, Zeta functions of formal languages. Trans. Amer. Math. Soc., 1990, 321, pp. 533-546. Zbl0797.68092 MR998123 Formal languages and automata, Semigroups in automata theory, linguistics, etc., Exact enumeration problems, generating functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Algebraic theory of languages and automata Zeta functions of formal languages | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces compact Riemann surfaces; complex function fields; abelian integrals; Jacobian variety; Abel-Jacobi map \textit{Iwasawa K.}, Algebraic Functions, Amer. Math. Soc., New York and Providence (1993) (Trans. Math. Monogr.; 188). Algebraic functions and function fields in algebraic geometry, Compact Riemann surfaces and uniformization Algebraic functions. Translated from the Japanese by Goro Kato | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative geometry; Hochshchild cohomology; Harrison cohomology; representation theory; obstruction theory; formally smooth algebras; finitely unobstructed algebras; moduli of representations A. Ardizzoni, F. Galluzzi and F. Vaccarino, A new family of algebras whose representation schemes are smooth, Ann. Inst. Fourier (Grenoble), 66 (2016), no. 3, 1261--1277. Singularities in algebraic geometry, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Rings arising from noncommutative algebraic geometry, Algebraic moduli problems, moduli of vector bundles A new family of algebras whose representation schemes are smooth | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite field; function field; asymptotically exact sequence; class number; tower of function fields Stéphane Ballet and Robert Rolland, Families of curves over any finite field attaining the generalized Drinfeld-Vladut bound, Actes de la Conférence ''Théorie des Nombres et Applications'', Publ. Math. Besançon Algèbre Théorie Nr., vol. 2011, Presses Univ. Franche-Comté, Besançon, 2011, pp. 5 -- 18 (English, with English and French summaries). Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Curves over finite and local fields, Finite ground fields in algebraic geometry Families of curves over any finite field attaining the generalized Drinfeld-Vladut bound | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic function fields; residue of differential form; system of parameters of valuation Kawahara, Y., Uchibori, T.: On residues of differential forms in algebraic function fields of two variables. TRU Math.17, 235--253 (1981) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Residues for several complex variables On resdiues of differential forms in algebraic function fields of two variables | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Krichever-Novikov algebras; applications to the geometry of moduli spaces; Knizhnik-Zamolodchikov equations; second-order Casimir operators of affine Krichever-Novikov algebras; fermion representations; semi-Casimirs; tangent spaces to the moduli spaces of Riemann surfaces Virasoro and related algebras, Applications of Lie (super)algebras to physics, etc., Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Drinfeld modules; elliptic modules; function fields; isogeny characters; torsion of Drinfeld modules Drinfel'd modules; higher-dimensional motives, etc., Rational points, Polynomials over finite fields, Arithmetic theory of algebraic function fields, Arithmetic aspects of modular and Shimura varieties, Special algebraic curves and curves of low genus, Abelian varieties of dimension \(> 1\) On isogeny characters of Drinfeld modules of rank two | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces surface; contact of surfaces; ruled surface; enumeration Surfaces in Euclidean and related spaces, Euclidean analytic geometry, Enumerative problems (combinatorial problems) in algebraic geometry A note concerning the theory of osculating surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces rank two vector bundles on algebraic surfaces; sheets; stratification of the moduli space; rational ruled surfaces Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Families, moduli, classification: algebraic theory On the cohomological strata of families of vector bundles on algebraic surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces automorphisms; survey; Riemann surfaces; algebraic function fields; Kummer extensions Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Automorphisms of algebraic function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tensor rank; bilinear complexity; finite fields; algebraic function fields Ballet, S.: A note on the tensor rank of the multiplication in certain finite fields, Ser. number theory appl. 5, 332-342 (2008) Applications to coding theory and cryptography of arithmetic geometry, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Algebraic coding theory; cryptography (number-theoretic aspects) A note on the tensor rank of the multiplication in certain finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite fields; number theory; algebraic geometry; permutation polynomials; multilinear equations; quadratic forms; characters; Gauss sums; Jacobi sums; diagonal equations; zeta function; Chevalley's theorem; law of quadratic reciprocity; Davenport-Hasse theorem; Fermat curve; elliptic curve Small, C.: Arithmetic of finite fields. Monogr. textbooks pure appl. Math. 148 (1991) Finite fields and commutative rings (number-theoretic aspects), Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Polynomials over finite fields, Quadratic forms over general fields, Other character sums and Gauss sums, Structure theory for finite fields and commutative rings (number-theoretic aspects), Finite ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Arithmetic of finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic geometry; Riemann hypothesis; function fields; Severi's algebraic theory of correspondences on algebraic curves André Weil [3] On the Riemann hypothesis in function-fields , Proceedings of the National Academy of Sciences, vol. 27 (1941), pp. 345-347. Duke University. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields On the Riemann hypothesis in function-fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces fields of characteristic 3; lines on quartic surfaces Rams, S.; Schütt, M., 112 lines on smooth quartic surfaces (characteristic 3), Q. J. Math., 66, 941-951, (2015) Special surfaces, \(K3\) surfaces and Enriques surfaces, Hypersurfaces and algebraic geometry, Varieties of low degree, Configurations and arrangements of linear subspaces 112 lines on smooth quartic surfaces (characteristic 3) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Grothendieck group of skew-symmetric spaces; Witt group; zero-cycles; rational equivalence; real affine surface Ojanguren, M; Parimala, R; Sridharan, R, Symplectic bundles over affine surfaces, Comment. Math. Helv., 61, 491-500, (1986) Picard groups, Applications of methods of algebraic \(K\)-theory in algebraic geometry, General binary quadratic forms, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Algebraic cycles, (Equivariant) Chow groups and rings; motives Symplectic bundles over affine surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric bialgebra; skew symmetric bialgebra; bialgebra of binary forms; bialgebra of ternary forms; semisimplicity; weak semisimplicity; apolarity; Salmon subalgebra; Wiman subalgebra M. Gizatullin, ``Bialgebra and geometry of plane quartics'', Asian J. Math., 5:3 (2001), 387 -- 432 Questions of classical algebraic geometry, Projective techniques in algebraic geometry, Plane and space curves Bialgebra and geometry of plane quartics. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces embeddings of algebraic surfaces in \(\mathbb{P}^ 4\); ruled surfaces Embeddings in algebraic geometry, Projective techniques in algebraic geometry, Rational and ruled surfaces Embeddings of algebraic surfaces in \(\mathbb{P}^ 4\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(\dagger\)-adic algebras; \(p\)-adic de Rham cohomology; \(p\)-adic de Rham complex; factorization of the zeta function; functoriality; group of automorphisms; transfer module; special module; \(p\)-adic differential operators; cohomological operations; flat liftings; \(\dagger\)-adic schemes; infinitesimal site; Gysin sequence; infinitesimal topos Arabia, A.; Mebkhout, Z., Sur le topos infinitésimal \textit{p}-adique d\(###\)un schéma lisse I, Ann. Inst. Fourier, 60, 6, 1905-2094, (2010) \(p\)-adic cohomology, crystalline cohomology, \(p\)-adic differential equations, Commutative rings of differential operators and their modules, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, de Rham cohomology and algebraic geometry, Finite ground fields in algebraic geometry Infinitésimal \(p\)-adic topos of a smooth scheme. I. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tower of function fields; number of rational places; Zink's bound Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry A note on a tower by Bassa, Garcia and Stichtenoth | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces diophantine equations; analogue of Thue equation; polynomial ring; diophantine approximation in fields of series; rational function solutions; first order algebraic differential equations \(p\)-adic and power series fields, Higher degree equations; Fermat's equation, Approximation in non-Archimedean valuations, Global ground fields in algebraic geometry Polynomial solutions of \(F(x,y)=z^n\). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces regular ruled surfaces; Hilbert scheme; stable ruled surfaces; moduli of abstract ruled surfaces E. Arrondo, M. Pedreira, I. Sols, On regular and stable ruled surfaces in P3. In: \textit{Algebraic curves and projective geometry (Trento}, 1988), volume 1389 of \textit{Lecture Notes in Math.}, 1-15, Springer 1989. MR1023385 Zbl 0694.14015 Rational and ruled surfaces, Families, moduli, classification: algebraic theory, Parametrization (Chow and Hilbert schemes) On regular and stable ruled surfaces in \({\mathbb{P}}^ 3\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(S\)-units in function fields; complement of a conic and two lines; log Kodaira dimension Corvaja, Pietro; Zannier, Umberto, Some cases of Vojta's conjecture on integral points over function fields, J. Algebraic Geom., 1056-3911, 17, 2, 295\textendash 333 pp., (2008) Varieties over global fields, Elliptic curves over global fields, Global ground fields in algebraic geometry Some cases of Vojta's conjecture on integral points over function fields. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic curves; complex multiplication; abelian varieties; zeta function; modular functions; theta functions; periods of integrals; class fields; field of moduli of a polarized abelian variety; Hecke \(L\)-functions; periods of abelian integrals; period symbol; differential forms; polarizations Shimura, G., \textit{abelian varieties with complex multiplication and modular functions}, (1998), Princeton University Press, Princeton, NJ Discontinuous groups and automorphic forms, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic moduli of abelian varieties, classification, Analytic theory of abelian varieties; abelian integrals and differentials, Complex multiplication and abelian varieties, Theta functions and abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Abelian varieties with complex multiplication and modular functions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces affine group schemes; category of commutative and cocommutative Hopf algebras; counitary \(K\)-coalgebras; internal Hom; Hopf algebra maps; right adjoint functor; tensor product of Hopf algebras; monoidal closed category Module categories in associative algebras, Group schemes, Abelian categories, Grothendieck categories The tensor product of Hopf algebras | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces rational function fields; moduli varieties of stable symplectic vector bundles; rationality Katsylo, PI, Birational geometry of moduli varieties of vector bundles over \({\mathbb{P}}^2\), Math. USSR-Izv., 38, 419-428, (1992) Families, moduli, classification: algebraic theory, Rational and unirational varieties, Algebraic moduli problems, moduli of vector bundles, Vector bundles on surfaces and higher-dimensional varieties, and their moduli Birational geometry of moduli varieties of vector bundles over \(\mathbb{P}^ 2\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces function fields; class group; continued fractions; generalization of Hirzebruch's theorem; class number González, CD, Class numbers of quadratic function fields and continued fractions, J. Number Theory, 40, 38-59, (1992) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Continued fractions, Jacobians, Prym varieties, Finite ground fields in algebraic geometry Class numbers of quadratic function fields and continued fractions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces connected semisimple Lie group; flag variety; Cartan subalgebra; twisted differential operators; enveloping algebra; infinitesimal character; localization function; topological tensor product; derived categories; derived functors of localization; equivalences of categories; Harish- Chandra modules; category of representations H. Hecht and J. Taylor, Analytic localization of representations, preprint. Semisimple Lie groups and their representations, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Universal enveloping (super)algebras, Lie algebras of Lie groups, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) Analytic localization of group representations | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces rational elliptic surfaces; del Pezzo surfaces; isotrivial rational elliptic surfaces; Zariski-density of rational points on algebraic varieties; points of an elliptic curve over a function field; root number of an elliptic curve Rational points, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces On the density of rational points on rational elliptic surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces quivers of type \(A\); representation spaces; Ringel-Hall algebras; canonical bases; categories of representations; symmetric functions; quantum groups; flag varieties; nilpotent orbits; Schubert varieties; Kazhdan-Lusztig polynomials; Schur-Weyl duality; affine Hecke algebras Schiffmann, O., Quivers of type \textit{A}, flag varieties and representation theory, Fields inst. commun., vol. 40, 453-479, (2004), Amer. Math. Soc. Providence, RI Representations of quivers and partially ordered sets, Grassmannians, Schubert varieties, flag manifolds, Quantum groups (quantized enveloping algebras) and related deformations, Hecke algebras and their representations, Symmetric functions and generalizations Quivers of type \(A\), flag varieties and representation theory. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tensor rank; real tensor rank; real symmetric tensor rank; additive decomposition of polynomials; typical rank Secant varieties, tensor rank, varieties of sums of powers, Multilinear algebra, tensor calculus, Real algebraic sets Partially complex ranks for real projective varieties | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces error-correcting code; \(C_{ab}\) curves; towers of algebraic function fields; genus Shor, Caleb McKinley, Genus calculations for towers of functions fields arising from equations of \(C_{ab}\) curves, Albanian J. Math., 5, 1, 31-40, (2011) Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry Genus calculations for towers of function fields arising from equations of \(C_{ab}\) curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces natural Lagrangian system; monoidal transformation of real analytic manifold; normal crossing; logarithmic fields; inversion of Lagrange-Dirichlet theorem; critical point; analytic potential function; Lyapunov's problem; supercritical motions; Lagrangian system with gyroscopic forces Palamodov, V.P.: Stability of motion and algebraic geometry. In: Dynamical Systems in Classical Mechanics (Amer. Math. Soc. Transl. Ser. 2), vol. 168, 5--20 (1995) Stability for nonlinear problems in mechanics, Global theory and resolution of singularities (algebro-geometric aspects) Stability of motion and algebraic geometry | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces real function fields; real holomorphy ring; valuation rings; formally real residue field; regular projective model; rational point; real prime divisors; signatures of higher level; sums of n-th powers; Local-Global- Principle; weak isotropy; quadratic forms; Henselizations SCHÜLTING, H.W.: Prime divisors on real varieties and valuation theory. J. Alg.98, 499-514 (1986) Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings Prime divisors on real varieties and valuation theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Pieri operators; Pieri formula; graded operation; Hopf algebra; quasi-symmetric functions; skew Schur functions; generating function; skew Schubert functions; Stanley symmetric functions; poset Bergeron, Mykytiuk, Sottile, and van Willigenburg, ''Non-commutative Pieri operators on posets,'' J. Combin. Th. Ser. A 91 (2000), 84--110. Symmetric functions and generalizations, Combinatorics of partially ordered sets, Classical problems, Schubert calculus Noncommutative Pieri operators on posets | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces compact Riemann surfaces; dessins d'enfants; fields of moduli; fields of definition; Shimura curves Arithmetic aspects of dessins d'enfants, Belyĭ theory, Modular and Shimura varieties, Dessins d'enfants theory, Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Fields of definition of uniform dessins on quasiplatonic surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hilbert scheme of smooth connected curves; regular components; ruled surfaces; double covers Parametrization (Chow and Hilbert schemes), Families, moduli of curves (algebraic) Components of the Hilbert scheme of smooth projective curves using ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces equivalence classes; nonsingular pencils of quadratic forms of even order; hyperelliptic function fields; norm map Quadratic forms over general fields, Algebraic functions and function fields in algebraic geometry Pencils of quadratic forms and hyperelliptic function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric polynomial of noncommutative variables; degree; Hessian; signature; eigenvalue H. Dym, J. W. Helton and S. McCullough, The Hessian of a non-commutative polynomial has numerous negative eigenvalues, Journal d'Analyse Mathématique 102 (2007), 29--76. Local spectral properties of linear operators, Real polynomials: analytic properties, etc., Multilinear and polynomial operators, Eigenvalues, singular values, and eigenvectors, Real algebraic and real-analytic geometry The Hessian of a noncommutative polynomial has numerous negative eigenvalues | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Schur polynomials; isotropic Grassmannians; degeneracy loci; image of a proper morphism; desingularization; skew-symmetric morphisms Pragacz, P. Cycles of Isotropic Subspaces And Formulas For Symmetric Degeneracy Loci. Topics in algebra, Part 2 (Warsaw, 1988), Banach Center Publ., vol. 26, pp. 189--199. PWN, Warsaw (1990). Rational and birational maps, Determinantal varieties, Grassmannians, Schubert varieties, flag manifolds, Quadratic spaces; Clifford algebras Cycles of isotropic subspaces and formulas for symmetric degeneracy loci | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces spacing distributions of zeros; zeros of the Riemann zeta-function; zeta functions of curves over finite fields; Montgomery-Odlyzko law; Ramanujan \(L\)-function; pair correlation; random matrix models; symplectic symmetry Katz, N.M., Sarnak, P.: Zeroes of zeta functions and symmetry. Bull. Am. Math. Soc. (N.S.) \textbf{36}(1), 1-26 (1999b) \(\zeta (s)\) and \(L(s, \chi)\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Other Dirichlet series and zeta functions, General mathematical topics and methods in quantum theory Zeroes of zeta functions and symmetry | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces graded ring; graded algebras; regular rings; noncommutative analogues of polynomial algebras; noetherian; global dimension Graded rings and modules (associative rings and algebras), Noetherian rings and modules (associative rings and algebras), Homological dimension in associative algebras, von Neumann regular rings and generalizations (associative algebraic aspects), Generalizations of commutativity (associative rings and algebras), Elliptic curves Regular rings of dimension three | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hilbert function of determinantal ideals; rings with straightening law; Hodge algebras Gräbe, H.-G.: Über Streckungsringe. Beiträge zur Algebra und Geometrie 23 (1986), 85-100. Polynomial rings and ideals; rings of integer-valued polynomials, Polynomials over commutative rings, Determinantal varieties Über Streckungsringe. (On rings with straightening law) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Drinfeld modular curve; expository paper; Shimura-Taniyama-Weil conjecture; function fields; rigid analytic geometry; Drinfeld modules of rank two; moduli space Gekeler ( E.U. ) and Reversat ( M. ) .- Some results on the Jacobians of Drinfeld modular curves , Preprint Univ. Toulouse 3 ( 1991 ). MR 1196521 Drinfel'd modules; higher-dimensional motives, etc., Jacobians, Prym varieties, Research exposition (monographs, survey articles) pertaining to number theory, Modular and Shimura varieties, Automorphic forms, one variable Some results on the Jacobians of Drinfeld modular curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cohomology theories of noncommutative operator algebras; Lie; algebra of infinite matrices of finite type; homological K-functor; \(C^*\)-algebras; Kasparov's KK-functor; cyclic homology; Gel'fand-Fuks cohomology theory of infinite-dimensional Lie; algebras; additive K-functor; derived functors; Chern characters; Bott periodicity; crystalline cohomology; differential graded algebra; de Rham complex; Gel'fand-Fuks cohomology theory of infinite-dimensional Lie algebras Feĭgin, Boris; Tsygan, Boris, Additive \(K\)-theory and crystalline cohomology, Funktsional. Anal. i Prilozhen., 19, 2, 52-62, 96, (1985) \(K\)-theory and operator algebras, Ext and \(K\)-homology, Kasparov theory (\(KK\)-theory), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Categories, functors in functional analysis, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), \(p\)-adic cohomology, crystalline cohomology, Cohomology of Lie (super)algebras, \(K\)-theory and operator algebras (including cyclic theory), Continuous cohomology of Lie groups, Resolutions; derived functors (category-theoretic aspects), Topological \(K\)-theory, Homology of classifying spaces and characteristic classes in algebraic topology, Homology and homotopy of \(B\mathrm{O}\) and \(B\mathrm{U}\); Bott periodicity, Graded rings and modules (associative rings and algebras), Classifying spaces for foliations; Gelfand-Fuks cohomology Additive \(K\)-theory and crystalline cohomology | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic curves over function fields; Mordell-Weil lattices; \(L\)-function of an elliptic curve over a function field T. Shioda, Some remarks on elliptic curves over function fields , Astérisque 209 (1992), 12, 99-114. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Rational points, Elliptic curves over global fields, Algebraic functions and function fields in algebraic geometry Some remarks on elliptic curves over function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces honeycombs; puzzles; hives; combinatorics of complex Grassmannians; additive and multiplicative Horn problems; Littlewood-Richardson coefficients; Gromov-Witten invariants; Knizhnik-Zamolodchikov equations; symmetric and affine symmetric groups; Hecke and Verlinde algebras; Kashivara crystals Veneziano Finite-dimensional groups and algebras motivated by physics and their representations, Combinatorial aspects of partitions of integers, Quantum groups and related algebraic methods applied to problems in quantum theory, \(2\)-body potential quantum scattering theory, Quantum groups (quantized enveloping algebras) and related deformations, Resonance in context of PDEs, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Heisenberg honeycombs solve Veneziano puzzle | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces rational points; homogeneous polynomial; quasi-projective variety; Hilbert subset; algebraic cycle with rational coefficients; finite fields; rationality of the zeta function of Hilbert sets; Dwork's rationality theorem; decomposition theorem Wan, Daqing: Hilbert sets and zeta functions over finite fields, J. reine angew. Math. 427, 193-207 (1992) Varieties over finite and local fields, Finite ground fields in algebraic geometry, Hilbertian fields; Hilbert's irreducibility theorem, Algebraic cycles Hilbert sets and zeta functions over finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces excellent function field; curve of genus 0; quadratic forms over function fields M. Rost, On quadratic forms isotropic over the function field of a conic, Mathematische Annalen 288 (1990), 511--513. Arithmetic theory of algebraic function fields, Quadratic forms over global rings and fields, Algebraic functions and function fields in algebraic geometry On quadratic forms isotropic over the function field of a conic | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite fields; character sums; Weil conjectures; Riemann-Roch theorem; points on curves over finite fields; zeta-functions; \(L\)-functions; idele class characters; modular forms; automorphic representations; Ramanujan graphs; Alon-Boppana theorem; regular graphs; Riemann hypothesis for zeta functions of curves over finite fields; exponential sums; Cayley graphs; finite upper half plane graphs; valuations of function fields; projective curve; Hecke operators; automorphic representations of quaternion groups; expander; simple random walk; spectral theory of graphs Li, W. -C. Winnie: Number theory with applications. Series of university mathematics 7 (1996) Research exposition (monographs, survey articles) pertaining to number theory, Modular and automorphic functions, Graph theory, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Representation-theoretic methods; automorphic representations over local and global fields, Holomorphic modular forms of integral weight, Estimates on exponential sums, Exponential sums, Adèle rings and groups, Representations of Lie and linear algebraic groups over global fields and adèle rings, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Number theory with applications | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces dilogarithm; \(K\)-theory of fields; hyperbolic geometry; Dedekind function; polylogarithms; motivic complexes; Zagier's conjecture; curves; regulators; special values of \(L\)-functions; motivic Lie algebra; framed mixed Tate motives; hyperlogarithms A. Goncharov, \textit{Polylogarithms in arithmetic and geometry}, \textit{Proc. ICM}\textbf{1-2} (1995) 374. Zeta functions and \(L\)-functions of number fields, \(K\)-theory of global fields, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Polylogarithms in arithmetic and geometry | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces infinite-dimensional Lie algebras; representations of the Witt algebra; symmetric polynomials; symmetric powers of curves; commuting operators; polynomial dynamical systems Lie algebras of vector fields and related (super) algebras, Applications of Lie algebras and superalgebras to integrable systems, Families, moduli of curves (algebraic), Plane and space curves, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Weierstrass statement; algebraic addition theorem; meromorphic functions; Picard varieties; continuation of closed subgroup; separately extendable meromorphic functions; algebraic function fields; quasi-abelian functions; extendable line bundles on toroidal groups Abe, Y., A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem, J. Math. Soc. Jpn., 57, 709-723, 07, (2005) Meromorphic functions of several complex variables, Abelian varieties and schemes A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebras; helices; projective spaces; Fano varieties; deformations; automorphisms of two-dimensional cubic curves A. I. Bondal and A. E. Polishchuk, Homological properties of associative algebras: the method of helices, Izv. Ross. Akad. Nauk Ser. Mat. 57 (1993), no. 2, 3 -- 50 (Russian, with Russian summary); English transl., Russian Acad. Sci. Izv. Math. 42 (1994), no. 2, 219 -- 260. Homological methods in associative algebras, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Representations of orders, lattices, algebras over commutative rings, Fano varieties Homological properties of associative algebras: The method of helices | 0 |
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