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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 set theoretic complete intersection curves; monoidal surfaces of degree 4 Complete intersections, Special surfaces, Curves in algebraic geometry Fourth degree monoidal surfaces of \({\mathbb{P}}^ 3_ k\) having complete intersection subset 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 decidability; Hilbert's Tenth Problem; uncomputably large integral points on algebraic curves; diophantine prefix; polynomials; height bounds; geometry of complex surfaces and 3-folds J.M. Rojas, Uncomputably large integral points on algebraic plane curves?, Theoret. Comput. Sci., 235 (this Vol.) (2000) 145--162. Decidability of theories and sets of sentences, Diophantine equations in many variables, Arithmetic problems in algebraic geometry; Diophantine geometry, Decidability (number-theoretic aspects), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Curves in algebraic geometry, Rational and ruled surfaces, Undecidability and degrees of sets of sentences Uncomputably large integral points on algebraic plane 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 surfaces of fourth and fifth degree; singularities Singularities of surfaces or higher-dimensional varieties, Special surfaces, Line geometries and their generalizations Sketch of recent researches on quartic and quintic 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 elliptic curves with complex multiplication; curves of genus 2; Jacobians; product surfaces; abelian variety; Humbert invariant; binary and ternary quadratic forms; idoneal numbers; mass formula Kani, E., Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms, J. Number Theory, 139, 138-174, (2014) Elliptic curves over global fields, Abelian varieties of dimension \(> 1\), Complex multiplication and moduli of abelian varieties, Forms of degree higher than two, Jacobians, Prym varieties Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms | 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 field of positive characteristic; arithmetic fundamental group; Galois representation; automorphic representation G. Böckle and C. Khare, Finiteness results for mod \(l\) Galois representations over function fields, Galois representations, Representation-theoretic methods; automorphic representations over local and global fields, Coverings of curves, fundamental group, Galois cohomology Mod \(\ell\) representations of arithmetic fundamental groups. I: An analog of Serre's conjecture for 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 locally symmetric varieties; compactifications; modular forms; \(K3\) surfaces Loo E. Looijenga, \emph Compactifications defined by arrangements II: locally symmetric varieties of type IV. Duke Math. J. \textbf 119 (2003), no. 3, 527--588 (see also arXiv:math/0201218). Moduli, classification: analytic theory; relations with modular forms, Automorphic functions in symmetric domains, Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(K3\) surfaces and Enriques surfaces, Relations with arrangements of hyperplanes Compactifications defined by arrangements. II: Locally symmetric varieties of type IV | 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 automorphism groups of \(K3\) surfaces; \(K3\) surfaces; lattice theory; singular \(K3\) surfaces Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(K3\) surfaces and Enriques surfaces, Automorphisms of surfaces and higher-dimensional varieties On the geometry of singular \(K3\) surfaces with discriminant 3, 4 and 7 | 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 problem; canonical form; linear automorphisms; monomial automorphisms; fields of rational functions; survey Hajja, M.: Linear and monomial automorphisms of fields of rational functions: some elementary issues, Algebra and number theory (2000) Inverse Galois theory, Research exposition (monographs, survey articles) pertaining to field theory, Transcendental field extensions, Actions of groups on commutative rings; invariant theory, Rationality questions in algebraic geometry Linear and monomial automorphisms of fields of rational functions: Some elementary issues | 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 finiteness of fundamental groups of open rational surfaces; fiber of morphism Gurjar, R.V., Zhang, D.-Q.: On the fundamental groups of some open rational surfaces. Math. Ann. 306, 15--30 (1996) Homotopy theory and fundamental groups in algebraic geometry, Rational and ruled surfaces, Rational and unirational varieties On the fundamental groups of some open 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 Igusa function; moduli space; Eisenstein series; abelian surfaces Bröker, R.; Lauter, K.: Evaluating igusa functions. Math. comp. 83, 2977-2999 (2014) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Moduli, classification: analytic theory; relations with modular forms Evaluating Igusa 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 Determinants; algebra; geometry; discussion of an equation of second degree; homogeneous coordinates; analytic criteria; plane sections of \(2^{\text{nd}}\) order surfaces; invariants of quadratic forms; plane curves of third order Determinants, permanents, traces, other special matrix functions, Equations in general fields, Plane and space curves, Rational and ruled surfaces, Quadratic and bilinear forms, inner products, Vector and tensor algebra, theory of invariants A new application of the determinants to algebra 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 degeneracy locus; Buchsbaum subvarieties of codimension 2; moduli spaces of K3 surfaces; unirational three-folds [C] Chang M.C.: Classification of Buchsbaum subvarieties of codimension 2 in projective space. J. reine angew. Math.401, 101--112 (1989) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Low codimension problems in algebraic geometry, Families, moduli, classification: algebraic theory, Projective techniques in algebraic geometry, Rational and unirational varieties, \(K3\) surfaces and Enriques surfaces Classification of Buchsbaum subvarieties of codimension 2 in projective space | 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; modular forms; \(p\)-adic cohomology; zeta function; elliptic surfaces Elliptic curves over global fields, Holomorphic modular forms of integral weight, \(p\)-adic cohomology, crystalline cohomology, Elliptic surfaces, elliptic or Calabi-Yau fibrations On Tate's conjecture for the elliptic modular surface of level \(N\) over a prime field of characteristic \(1\mod N\) | 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 degeneration of Riemann surfaces; topological monodromy; pseudo-periodic homeomorphism Structure of families (Picard-Lefschetz, monodromy, etc.), Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants, Families, moduli of curves (analytic), Fibrations, degenerations in algebraic geometry Monodromies of splitting families for degenerations of Riemann 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 Kronecker series; \(L\)-functions of symmetric powers of elliptic curves; Beilinson's conjecture; motivic cohomology groups; Bloch-Beilinson regulator; de Rham cohomology Mestre, J. -F.; Schappacher, N.: Séries de Kronecker et fonctions L des puissances symétriques de courbes elliptiques sur Q. Progr. math. 89, 209-245 (1991) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Generalizations (algebraic spaces, stacks), (Co)homology theory in algebraic geometry Kronecker series and \(L\)-functions of symmetric powers of elliptic curves over \(\mathbb{Q}\) | 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 abelian varieties over arithmetic ground fields; moduli of abelian varities; Dieudonné modules Algebraic moduli of abelian varieties, classification, Abelian varieties of dimension \(> 1\), Formal groups, \(p\)-divisible groups, Arithmetic ground fields for abelian varieties The \(a\)-number stratification on the moduli space of supersingular abelian 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 domain of periods; Torelli theorem; Kählerian K 3 surfaces; Hodge isometry; marked K 3 surface A. Beauville, Préliminaires sur les périodes des surfaces K3 , Astérisque 126 (1985), 91-97. Special surfaces, Transcendental methods, Hodge theory (algebro-geometric aspects), Period matrices, variation of Hodge structure; degenerations, Compact complex surfaces Préliminaires sur les périodes des surfaces K 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 third moment of Kloosterman sums; number of rational points on smooth projective surfaces Gauss and Kloosterman sums; generalizations, Exponential sums, \(K3\) surfaces and Enriques surfaces, Trigonometric and exponential sums (general theory) The geometry of the third moment of exponential sums | 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 \(K3\) surfaces; modular forms on symmetric domains \(K3\) surfaces and Enriques surfaces, Holomorphic modular forms of integral weight, Automorphic functions in symmetric domains Inverse period mappings of \(K3\) surfaces and a construction of modular forms for a lattice with the Kneser conditions | 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 Moduli space; Riemann surface; Fuchsian group; strata of Riemann surfaces Costa, A. F., Izquierdo, M.: Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 4. In: Geometry of Riemann surfaces, London Math. Soc. Lecture Note Ser., 368, Cambridge Univ. Press, Cambridge, 2010, 120--138 Compact Riemann surfaces and uniformization, Automorphisms of curves, Fuchsian groups and their generalizations (group-theoretic aspects) Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 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 Brauer group of rational function field over complex field Brauer groups of schemes, Galois cohomology Groupe de Brauer et topologie des variétés algébriques complexes lisses. (Brauer group and topology of smooth complex algebraic 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 arithmetic zeta functions; foliated space; \(L\)-functions of number fields Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Foliations in differential topology; geometric theory, Zeta functions and \(L\)-functions of number fields On the analogy between arithmetic geometry and foliated spaces | 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 multilinear algebra; tensor calculus; computational aspects of algebraic; algebraic geometry Multilinear algebra, tensor calculus, Algebraic systems of matrices, Vector and tensor algebra, theory of invariants, Effectivity, complexity and computational aspects of algebraic geometry, Fano varieties, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Numerical algebraic geometry Ideals of spaces of degenerate matrices | 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 equivariant compactification; symmetric varieties; character sheaves; finite groups of Lie type Semisimple Lie groups and their representations, Group varieties Compactifications of symmetric varieties and applications to 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 diagonal equations; cyclotomic classes; cyclotomic numbers; number of points on finite diagonal curves; finite fields Curves over finite and local fields, Cyclotomy, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Counting the number of points on affine diagonal 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 quotient of complex surface under the action of automorphism group; Enriques surfaces Mukai, [Mukai and Namikawa 84] S.; Namikawa, Y., Automorphisms of Enriques surfaces which act trivially on the cohomology groups., \textit{Invent. Math.}, 77, 383-397, (1984) Homogeneous spaces and generalizations, Special surfaces, Group actions on varieties or schemes (quotients), Rational and birational maps Automorphisms of Enriques surfaces which act trivially on the cohomology groups | 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 varieties over a finite fields; zeta functions; bielliptic surfaces; albanese mapping; elliptic curves; étale cohomology; Frobenius morphism; isogeny class Рыбаков, С. Ю., Дзета-функции биэллиптических поверхностей над конечными полями, Матем. заметки, 83, 2, 273-285, (2008) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Zeta functions and \(L\)-functions, Finite ground fields in algebraic geometry Zeta functions of bielliptic surfaces 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 linear derivations; Lie algebra; formal differential operators; tensor algebra; Gelfand-Kirillov dimension; symmetric algebra; smooth affine variety; global differential operators S. P. Smith, Gel\(^{\prime}\)fand-Kirillov dimension of rings of formal differential operators on affine varieties, Proc. Amer. Math. Soc. 90 (1984), no. 1, 1 -- 8. Chain conditions on annihilators and summands: Goldie-type conditions, Automorphisms and endomorphisms, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Rings with involution; Lie, Jordan and other nonassociative structures, Morphisms of commutative rings, Automorphisms, derivations, other operators for Lie algebras and super algebras, Modules of differentials Gelfand-Kirillov dimension of rings of formal differential operators on affine 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 compact Riemann surfaces; vector bundles; ruled manifold; extension; fundamental group; representation; moduli Compact Riemann surfaces and uniformization, Sheaves and cohomology of sections of holomorphic vector bundles, general results, Vector bundles on curves and their moduli Vector bundles over compact Riemann 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) Kronecker coefficients; non saturation; geometric complexity theory; orbit closure of the determinant Symmetric groups, Representations of finite symmetric groups, Representation theory for linear algebraic groups, Geometric invariant theory Vanishing symmetric Kronecker coefficients | 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 algebraic curves; Kadomtsev-Petviashvili equations; Schottky's problem; symmetric Riemann surfaces Theta functions and curves; Schottky problem, Differentials on Riemann surfaces, Partial differential equations of mathematical physics and other areas of application Periodic solitons and real algebraic 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 Brauer groups of fields of invariants; Galois cohomology; Artin-Mumford group of the field of rational functions Bogomolov F.A., Brauer groups of fields of invariants of algebraic groups, Math. USSR-Sb., 1990, 66(1), 285--299 Geometric invariant theory, Galois cohomology, Brauer groups of schemes, Group actions on varieties or schemes (quotients), Actions of groups on commutative rings; invariant theory Brauer groups of fields of invariants of algebraic groups | 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 textbook (functions of complex variables); Riemann surfaces; harmonic functions; uniformization; functions of several complex variables; abelian functions; modular forms Freitag B., Complex Analysis (2009) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable, Riemann surfaces, Holomorphic functions of several complex variables, Analytic theory of abelian varieties; abelian integrals and differentials, Modular and automorphic functions, Holomorphic modular forms of integral weight, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Theta series; Weil representation; theta correspondences Function theory 2. Riemann surfaces, several complex variables, abelian functions, higher modular forms | 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 abstract elliptic function fields; automorphisms; meromorphisms; addition theorem Hasse, H.: Zur theorie der abstrakte elliptischen funktionenkörper. II. automorphismen und meromorphismen. Das additionstheorem. J. reine angrew. Math. 175, 69-88 (1936) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Theorie der abstrakten elliptischen Funktionenkörper. II: Automorphismen und Meromorphismen. Das Additionstheorem | 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 d-gonal curve of genus g; nodes; rational surfaces; unirational Hurwitz spaces Enrico Arbarello and Maurizio Cornalba. Footnotes to a paper of {B}eniamino {S}egre: ``{O}n the modules of polygonal curves and on a complement to the {R}iemann existence theorem'' ({I}talian) [{M}ath. {A}nn. 100 (1928), 537--551; {J}buch 54, 685]. Math. Ann., 256(3):341--362, 1981. The number of \(g{1}{d}\)'s on a general \(d\)-gonal curve, and the unirationality of the Hurwitz spaces of \(4\)-gonal and \(5\)-gonal curves. DOI 10.1007/BF01679702; zbl 0454.14023; MR0626954 Enumerative problems (combinatorial problems) in algebraic geometry, Rational and unirational varieties, Special algebraic curves and curves of low genus Footnotes to a paper of Beniamino Segre. (The number of \(g^1_d\)'s on a general \(d\)-gonal curve, and the unirationality of the Hurwitz spaces of 4-gonal and 5-gonal 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 deformations of tetragonal canonical curves; projective extensions; complete intersections on scrolls; rolling deformations; \(K3\) surfaces Stevens J., Rolling factors deformations and extensions of canonical curves, Doc. Math. 6 (2001), 185-226, electronic. Special divisors on curves (gonality, Brill-Noether theory), \(K3\) surfaces and Enriques surfaces, Deformations of complex singularities; vanishing cycles, Deformations of singularities, Formal methods and deformations in algebraic geometry Rolling factors deformations and extensions of canonical 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 split octonion algebra; automorphism group; Lie group of type \(G_2\); symmetric rooms; Bruhat-Tits buildings; standard apartment; Arakelov bundles; invariant flag Composition algebras, Group schemes, Root systems, Groups with a \(BN\)-pair; buildings, Representation theory for linear algebraic groups, Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) Octonions and reduction 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 tautological rings; moduli spaces of curves; Chow motives; twisted commutative algebras Families, moduli of curves (algebraic), Algebraic cycles, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Classifying spaces of groups and \(H\)-spaces in algebraic topology Tautological classes with twisted coefficients | 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 algebraic geometry; real algebraic varieties; complexification; Smith's theory; Galois-Maximal varieties; algebraic cycles; real algebraic models; algebraic curves; algebraic surfaces; topology of algebraic varieties; regular maps; rational maps; singularities; algebraic approximation; Comessatti theorem; Rokhlin theorem; Nash conjecture; Hilbert's XVI problem; Cremona group; real fake planes Topology of real algebraic varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Real algebraic and real-analytic geometry, Surfaces and higher-dimensional varieties, Curves in algebraic geometry, Varieties and morphisms, Special varieties Real algebraic 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 irregular surfaces; classification of hyperelliptic surfaces C. Ciliberto, M. de Franchis and the theory of hyperelliptic surfaces, Studies in the history of modern mathematics, III, Rend. Circ. Mat. Palermo (2)(Suppl. 55) (1998) 45-73. Special surfaces, History of mathematics in the 20th century, History of algebraic geometry M. de Franchis and the theory of hyperelliptic 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 Shafarevich complexes; noncommutative complete intersections; homology algebras E. S. Golod, ''Homologies of the Shafarevich complex and noncommutative complete intersections,'' Fund. Prikl. Mat., 5, No. 1, 85--95 (1999). Syzygies, resolutions, complexes in associative algebras, Differential graded algebras and applications (associative algebraic aspects), Linkage, complete intersections and determinantal ideals, Complete intersections, Rings arising from noncommutative algebraic geometry Homology of the Shafarevich complex and noncommutative complete intersections | 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 arithmetic function; number of factorizations of an integer; group of rational points; elliptic curves Arithmetic functions; related numbers; inversion formulas, Cubic and quartic Diophantine equations, Elliptic curves Some arithmetic functions associated with diophantine 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 noncommutative algebraic geometry; spectrum of an abelian category; localizations; canonical topologies A. L. Rosenberg, Noncommutative local algebra, Geometric and Functional Analysis 4 (1994), 545--585. Noncommutative algebraic geometry, Abelian categories, Grothendieck categories, Localization of categories, calculus of fractions Noncommutative local algebra | 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 root number; fibers of elliptic surfaces E. Manduchi. Root Numbers of fibers of elliptic surfaces. Compositio Math., 99(1) (1995), 33--58. Elliptic surfaces, elliptic or Calabi-Yau fibrations, Families, fibrations in algebraic geometry Root numbers of fibers of 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 ordinary K3 surfaces; finite fields \(K3\) surfaces and Enriques surfaces, Finite ground fields in algebraic geometry Ordinary K3 surfaces over a finite field | 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 Kummer surfaces; resolving singularities of the quotient of a complex torus by a finite abelian group; Euler numbers; toroidal desingularization; string J. Halverson, C. Long and B. Sung, \textit{Algorithmic universality in F-theory compactifications}, \textit{Phys. Rev.}\textbf{D 96} (2017) 126006 [arXiv:1706.02299] [INSPIRE]. Special surfaces, Global theory and resolution of singularities (algebro-geometric aspects), Topological properties in algebraic geometry On the generalization of Kummer 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 generalization of class field theory; local fields; Milnor K-group; integral projective scheme; Chow group; generalization of ramification theory; higher dimensional schemes; generalized Swan conductor; global fields Class field theory, Class field theory; \(p\)-adic formal groups, Higher symbols, Milnor \(K\)-theory, \(K\)-theory of global fields, \(K\)-theory of local fields, Ramification and extension theory, Formal groups, \(p\)-divisible groups, Generalized class field theory (\(K\)-theoretic aspects) Generalization of class field 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 rings of differential operators; semisimple Lie algebras; gluing of categories DOI: 10.1017/S1474748002000154 Rings of differential operators (associative algebraic aspects), Homogeneous spaces and generalizations, Eilenberg-Moore and Kleisli constructions for monads Gluing of Abelian categories and differential operators on the basic affine space. | 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 moduli spaces; surfaces; surfaces of general type; volumes of divisors; slc pairs Surfaces of general type, Families, moduli, classification: algebraic theory, Divisors, linear systems, invertible sheaves On the boundedness of slc surfaces of general type | 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 fundamental group; ovals; K3 surfaces; monodromy groups of smooth real plane curves of degree 6 I. Itenberg, Groups of monodromy of non-singular curves of degree 6, Real Analytic and Algebraic Geometry, Proceedings, Trento (Italy) 1992, Walter de Gruyter, (1995), 161--168. Special algebraic curves and curves of low genus, Real algebraic sets Groups of monodromy of non-singular curves of degree 6 | 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 semi-algebraic sets; real algebraic varieties; rational points; generalized Teichmüller space; moduli of compact Riemann surfaces; Fricke moduli Kyoji Saito: Algebraic Representation of the Teichmuller Spaces, The Grothendieck Theor of Dessins dnfants, Edited by L. Schneps, London Math. Soc. Lee. Note Ser. 200, Cambridge Univ. Press, 1994. Families, moduli of curves (analytic), Compact Riemann surfaces and uniformization, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Algebraic representation of the Teichmüller spaces | 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 Borel conjecture; \(L^ 2\)-cohomology of locally symmetric varieties; modular curves; automorphic forms; intersection cohomology; Zucker conjecture Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) A brief introduction to the \(L^ 2\)-cohomology of locally symmetric 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 surfaces of 4th order; pencils of surfaces of 2nd order Families, moduli, classification: algebraic theory, Euclidean analytic geometry Note on the surfaces of the fourth order | 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 \(K3\) surfaces; Weierstrass equations; elliptic fibrations; elliptic fibrations of \(K3\) surfaces Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(K3\) surfaces and Enriques surfaces, Elliptic curves over global fields Weierstrass equations for the elliptic fibrations of a \(K3\) surface | 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 non-associative algebras; problem of Albert; invariant bilinear forms; nil-algebras; solvable algebras; polynomial endomorphisms; Jacobian conjecture Power-associative rings, Structure theory for nonassociative algebras, Automorphisms, derivations, other operators (nonassociative rings and algebras), Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Jacobian problem The space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism: an approach to the problem of Albert | 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 semigroups of pointed curves; double coverings of curves; curves on \(K3\) surfaces Watanabe, K, An example of the Weierstrass semigroup of a pointed curve on K3 surfaces, Semigroup Forum, 86, 395-403, (2013) Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, \(K3\) surfaces and Enriques surfaces An example of the Weierstrass semigroup of a pointed curve on \(K3\) 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 automorphisms of compact Riemann surfaces; theta functions Automorphisms of curves, Theta functions and curves; Schottky problem Analytic computation of some automorphism groups of Riemann 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 partial ordering; partitions; specialization order; permutation representations; symmetric groups; orbits of nilpotent matrices; Gale-Ryser theorem M. Hazewinkel and C. Martin, ''Representations of the symmetric group, the specialization order, systems and the Grassmann manifold,''L'Enscign. Math.,29, 53--87 (1983). Representations of finite symmetric groups, Partial orders, general, Combinatorial aspects of partitions of integers, Grassmannians, Schubert varieties, flag manifolds, Group actions on varieties or schemes (quotients) Representations of the symmetric group, the specialization order, systems and Grassmann 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 cyclotomic function fields; algebraic curve over a finite field; \(L\)-functions Goss, D., On a new type of \textit{L}-functions for algebraic curves over finite fields, Pacific J. math., 105, 143-181, (1983) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On a new type of \(L\)-function for algebraic curves 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 quantum groups; roots of unity; localization; derived equivalence; Calabi-Yau categories; noncommutative algebraic geometry E. Backelin and K. Kremnizer, ''Localization for quantum groups at a root of unity,'' J. Amer. Math. Soc., vol. 21, iss. 4, pp. 1001-1018, 2008. Noncommutative algebraic geometry, Quantum groups (quantized enveloping algebras) and related deformations, Geometry of quantum groups, Quantum groups (quantized function algebras) and their representations Localization for quantum groups at a root of unity | 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 finite fields; zeta-functions of curves; Abelian varieties over finite fields Katz, N.: Spacefilling curves over finite fields. Mrl 6, 613-624 (1999) Curves over finite and local fields, Finite ground fields in algebraic geometry, Abelian varieties of dimension \(> 1\), Varieties over finite and local fields Space filling curves 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 difference field; abelian variety; theory ACFA; group definable in a model; model theoretic stability; 1-basedness; Manin-Mumford conjecture; model companion of the theory of fields with an automorphism Z. Chatzidakis, ''Groups definable in ACFA,'' in Algebraic Model Theory, Dordrecht: Kluwer Acad. Publ., 1997, vol. 496, pp. 25-52. Model-theoretic algebra, Applications of logic to group theory, Model theory of fields, Difference algebra, Classification theory, stability, and related concepts in model theory, Abelian varieties of dimension \(> 1\), Rational points Groups definable in ACFA | 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 number of non-rational subfields; number of separable subfields; number of morphisms of algebraic curves; Chow coordinates; theorem of the base; Jacobian; genus; function field; Angle theorem; de Franchis' theorem E. Kani, Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. Zbl0615.12017 MR842053 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Birational geometry, Jacobians, Prym varieties, Divisors, linear systems, invertible sheaves, Special surfaces Bounds on the number of non-rational subfields of a function field | 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; automorphism groups; cohomology Cai, J.-X., Automorphisms of an irregular surface of general type acting trivially in cohomology, J. Algebra, 367, 95-104, (2012) Automorphisms of surfaces and higher-dimensional varieties, Surfaces of general type Automorphisms of an irregular surface of general type acting trivially in 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 modular QM-abelian surfaces; newform of weight two; quaternion algebra; quaternion multiplication; quaternion division algebra DOI: 10.3792/pjaa.72.23 Holomorphic modular forms of integral weight, Complex multiplication and abelian varieties, Complex multiplication and moduli of abelian varieties On some examples of modular QM-abelian 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 Hasse-Weil bound; trace code; Hamming weight; algebraic curves over finite fields of characteristic 2; number of points van der Geer, Gerard; van der Vlugt, Marcel, Curves over finite fields of characteristic 2 with many rational points, C. R. acad. sci. Paris Sér. I math., 317, 6, 593-597, (1993), MR 1240806 Finite ground fields in algebraic geometry, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Rational points, Linear codes (general theory) Curves over finite fields of characteristic 2 with many rational 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 birational anabelian; algebraically closed fields; absolute Galois group; function fields; Galois-type correspondence Elliptic curves over global fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Algebraic functions and function fields in algebraic geometry A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary 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 algebraic group schemes; non-reduced group schemes; minimal splitting fields; Galois groups; coordinate rings; groups of rational characters; maximal tori; connected unipotent groups; products of reductions Linear algebraic groups over local fields and their integers, Varieties over global fields, Group schemes Galois lattices and reductions of algebraic tori. | 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 jet spaces; prolongations of diffeomorphisms; foliated G-actions; Hessian matrices; affine and special affine transformations; recurrence relations; commutators of invariant differentials; classification of developable surfaces; homogeneous models Differential invariants (local theory), geometric objects, Local submanifolds, Affine differential geometry, Curves in Euclidean and related spaces, Surfaces in Euclidean and related spaces, Normal forms on manifolds, Computational methods for problems pertaining to differential geometry, Actions of groups and semigroups; invariant theory (associative rings and algebras), Group actions on affine varieties, Local Lie groups, Symmetries, invariants, etc. in context of PDEs On differential invariants of parabolic 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 Galois lattice structure of the Mordell-Weil group; height pairing; L-function; Hasse zeta function; computer calculations Shioda, T.: The Galois Representations of TypeE 8 Arising from Certain Mordell-Weil Groups, Proc. Japan Acad.65A, 195--197 (1989) Rational points, Elliptic curves, Computational aspects of algebraic curves The Galois representation of type \(E_8\) arising from certain Mordell-Weil groups | 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 regular rings; cyclic quotient singularities; rational double points; rings of invariants; local dualities; dualizing complexes; Gorenstein singularities; Cohen-Macaulay singularities Chan, D.: Noncommutative rational double points. J. algebra 232, 725-766 (2000) Rings arising from noncommutative algebraic geometry, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting), Rational and ruled surfaces, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Actions of groups and semigroups; invariant theory (associative rings and algebras), Valuations, completions, formal power series and related constructions (associative rings and algebras), Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Representation type (finite, tame, wild, etc.) of associative algebras, Cohen-Macaulay modules in associative algebras Noncommutative rational double 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 ruled surfaces; Einstein-Maxwell metrics; conformally Kähler metrics Koca, C.; Tønnesen-Friedman, CW, Strongly Hermitian Einstein-Maxwell solutions on ruled surfaces, Ann. Glob. Anal. Geom., 50, 29-46, (2016) Global differential geometry of Hermitian and Kählerian manifolds, Rational and ruled surfaces, Special Riemannian manifolds (Einstein, Sasakian, etc.), Applications of global differential geometry to the sciences, Exact solutions to problems in general relativity and gravitational theory, Einstein-Maxwell equations Strongly Hermitian Einstein-Maxwell solutions on 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 stable surface; stable log surface; surface of general type; geography of surfaces; moduli of surfaces of general type Liu, W.; Rollenske, S., Geography of Gorenstein stable log surfaces[J], \textit{Trans, Amer. Math. Soc.}, 368, 4, 2563-2588, (2013) Families, moduli, classification: algebraic theory, Surfaces of general type, Singularities of surfaces or higher-dimensional varieties Geography of Gorenstein stable log 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 Belyi function; Belyi's theorem; Belyi surface; dessins d'enfants; Riemann surfaces Singerman, D; Bujalance, E (ed.); Costa, AF (ed.); Martínez, E (ed.), Riemann surfaces, Belyi functions and hypermaps, 43-68, (2001), Cambridge Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) Riemann surfaces, Belyi functions and hypermaps | 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 Gorenstein Artin algebras; Hilbert function; codimension four Gorenstein Artin algebra DOI: 10.2140/pjm.1999.187.1 Cohen-Macaulay modules, Commutative Artinian rings and modules, finite-dimensional algebras, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) Components of the space parametrizing graded Gorenstein Artin algebras with a given Hilbert 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 complex suspension theorem; Lawson homology; generalized cycle map; joins of algebraic cycles; integral currents; Thom isomorphisms; generalized flag varieties; compact hermitian symmetric spaces; reductive group action Lima-Filho P.: On the generalized cycle map. J. Differ. Geom. 38, 105--130 (1993) (Co)homology theory in algebraic geometry, Algebraic cycles, Other homology theories in algebraic topology, Homotopy theory and fundamental groups in algebraic geometry On the generalized cycle map | 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 infinitesimal Schur algebras; quantum Schur algebras; blocks; polynomial representations; Frobenius kernels; general linear groups; monoids of matrices; monoid schemes; rational representations Cox A.G.: On the blocks of the infinitesimal Schur algebras. Quart. J. Math 51, 39--56 (2000) Representation theory for linear algebraic groups, Representation of semigroups; actions of semigroups on sets, Group schemes, Quantum groups (quantized enveloping algebras) and related deformations, Quantum groups (quantized function algebras) and their representations On the blocks of the infinitesimal Schur 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 poles of Igusa's local zeta function; resolution of singularities Veys, W.: On the poles of Igusa's local zeta function for curves. J. Lond. Math. Soc. 41, 27--32 (1990) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Zeta functions and \(L\)-functions On the poles of Igusa's local zeta function for 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 conjugates of equivariant holomorphic maps of symmetric domains; arithmetic varieties; Kuga fiber variety Lee, Pacific J. Math. 149 pp 127-- (1991) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Varieties over global fields, Arithmetic ground fields for abelian varieties Conjugates of equivariant holomorphic maps of symmetric domains | 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 semigroup of integral points; convex body; graded algebra; Hilbert function; Hodge index theory; mixed volume; Alexandrov-Fenchel inequality; Bernstein-Kushnirenko theorem; Cartier divisor; linear series Kaveh, K. and Khovanskii, A., Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, \textit{Ann. of Math. (2)}176 ( 2012), no. 2, 925- 978. Homogeneous spaces and generalizations, Toric varieties, Newton polyhedra, Okounkov bodies Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection 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 Hilbert function; zero-dimensional subscheme; number of points; Castelnuovo sets DOI: 10.1016/S0022-4049(97)00164-3 Low codimension problems in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Projective techniques in algebraic geometry Extremal zero-dimensional subschemes of \({\mathbb{P}}^2\) | 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 surfaces of general type; rational points; Bombieri-Lang conjecture; Erdős problems in discrete geometry; rational distances Arithmetic algebraic geometry (Diophantine geometry), Rational points, Surfaces of general type, Erdős problems and related topics of discrete geometry A solution of the Erdős-Ulam problem on rational distance sets assuming the Bombieri-Lang conjecture | 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 Gorenstein algebras; unimodal \(h\)-sequences; Hilbert series; graded ring; linkage class of a complete intersection Beintema, M. B.: Gorenstein algebras with unimodal h-sequences. Comm. algebra 20, 979-997 (1992) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Graded rings, Linkage, complete intersections and determinantal ideals, Linkage Gorenstein algebras with unimodal \(h\)-sequences | 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 hyperplane sections of surfaces; linear series; adjunction map Divisors, linear systems, invertible sheaves, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Complete intersections, Special surfaces Curves and \(0\)-cycles on projective 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 formal characters of torus; connected, reductive algebraic group; Borel subgroup; character group; Hochschild cohomology; Weyl's character formula; Kostant's multiplicity formula; Steinberg's tensor product formula Cohomology theory for linear algebraic groups, Representation theory for linear algebraic groups, Classical groups (algebro-geometric aspects) A new proof of old character formulas | 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 polynomial ring; monomials; Veronese subrings; regularity of ideal; Gröbner basis; homogeneous Koszul algebras Fröberg, R.: Koszul algebras. In: Advances in commutative ring theory (Fez, 1997) Lecture Notes in Pure and Appl. Math., vol. 205, pp. 337-350. Dekker, New York (1999) Polynomial rings and ideals; rings of integer-valued polynomials, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Linkage, complete intersections and determinantal ideals Initial ideals, Veronese subrings, and rates of 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 moduli space of stable curves; homotopy type of moduli space; Satake compactification of the Siegel modular varieties; period mapping; Riemann surfaces; period matrices Families, moduli of curves (algebraic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Classification of homotopy type, Period matrices, variation of Hodge structure; degenerations, Compactification of analytic spaces Moduli space of stable curves from a homotopy viewpoint | 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 existence of moduli space for elliptic surface; global coarse moduli; genus; invariant theory; elliptic surfaces with a section W.K. Seiler : Global moduli for elliptic surfaces with a section , Comp. Math. 62 (1987) 169-185. Families, moduli, classification: algebraic theory, Algebraic moduli problems, moduli of vector bundles, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Fine and coarse moduli spaces Global moduli for elliptic surfaces with a section | 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; symmetric polynomials; singular locus; rational solutions; diagonal equations Polynomials over finite fields, Symmetric functions and generalizations, Rational points, Finite ground fields in algebraic geometry, Varieties over finite and local fields Estimates on the number of \(\mathbb{F}_q\)-rational solutions of variants of diagonal equations 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 conjecture of Beilinson and Bloch; rank of the Griffiths group; smooth projective variety over a number field; order of vanishing of an L-function; elliptic curves J. Buhler, C. Schoen, and J. Top, ''Cycles, \(L\)-functions and triple products of elliptic curves,'' J. reine angew. Math., vol. 492, pp. 93-133, 1997. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Varieties over global fields, Algebraic cycles, Global ground fields in algebraic geometry Cycles, \(L\)-functions and triple products of elliptic 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 integrable systems; Picard group; Riemann surfaces of infinite genus; complete integrability; eigenbundles; holomorphic line bundles; spectral curve; divisors; Darboux coordinates; Serre duality Schmidt M U 1996 \textit{Integrable Systems and Riemann Surfaces of Infinite Genus}\textit{(Memoirs of the American Mathematical Society vol 122)} (Providence, RI: American Mathematical Society) pp 1--111 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.), Singularities of curves, local rings, Theta functions and curves; Schottky problem, NLS equations (nonlinear Schrödinger equations) Integrable systems and Riemann surfaces of infinite genus | 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 deformation of complex structures; moduli spaces for Hopf surfaces Deformations of complex structures, Compact complex surfaces, Complex-analytic moduli problems, Algebraic moduli problems, moduli of vector bundles, Fine and coarse moduli spaces Classification and deformation of complex structures on \(S^ 1\times S^ 3.\) Kuranishi families and moduli spaces for Hopf 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 deformation theory; Higgs field; surfaces; positive canonical bundle; stable torsion sheaves; symmetric perfect obstruction theory; moduli space; \(\operatorname{SU}(r)\) Vafa-Witten invariants; Euler characteristic; nested Hilbert schemes Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Symplectic structures of moduli spaces Vafa-Witten invariants for projective surfaces. I: Stable case | 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 local Hilbert's 16th problem; Nash space of arcs; planar quadratic vector fields; essential perturbation Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Arcs and motivic integration, Bifurcation theory for ordinary differential equations Hilbert's 16th problem on a period annulus and Nash space of arcs | 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 flag manifolds; symmetric group; root systems; Schubert cells; homology; height of roots; boundary coefficients Homology and cohomology of homogeneous spaces of Lie groups, Permutations, words, matrices, Grassmannians, Schubert varieties, flag manifolds, Root systems A correspondence between boundary coefficients of real flag manifolds and height of roots | 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 function; Schubert polynomials; Schur polynomials; Schubert functions; Baxter operator; reduced words of permutations Winkel, R.: Schubert functions and the number of reduced words of permutations, Sém. lothar. Combin. 39, 1-28 (1997) Reflection and Coxeter groups (group-theoretic aspects), Grassmannians, Schubert varieties, flag manifolds Schubert functions and the number of reduced words of permutations | 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 Hodge theory; cyclic homology; cohomology of Lie algebras; Hochschild homology; de Rham cohomology; Loday conjecture Transcendental methods, Hodge theory (algebro-geometric aspects), Cohomology of Lie (super)algebras, \(K\)-theory and homology; cyclic homology and cohomology, de Rham cohomology and algebraic geometry, Loop groups and related constructions, group-theoretic treatment, Homological methods in Lie (super)algebras Some Hodge theory from Lie 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 finite fields; Reed-Solomon codes; deep holes; symmetric polynomials; singular hypersurfaces; rational points Cafure, A.; Matera, G.; Privitelli, M.: Singularities of symmetric hypersurfaces and Reed-Solomon codes. Adv. math. Commun. 6, No. 1, 69-94 (2012) Applications to coding theory and cryptography of arithmetic geometry, Symmetric functions and generalizations, Algebraic coding theory; cryptography (number-theoretic aspects), Combinatorial codes Singularities of symmetric hypersurfaces and Reed-Solomon 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 number fields; function fields G. Lustig, Über die Zetafunktion einer arithmetischen Mannigfaltigkeit. Math. Nachr.14, 309--330 (1956). Arithmetic varieties and schemes; Arakelov theory; heights, Zeta and \(L\)-functions: analytic theory On the zeta function of an arithmetic manifold. | 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 operator colligations; operator vessels; Livsic characteristic function; invariant subspaces; rational functions of operators Kravitsky, N, No article title, Integral Equations Operator Theory, 26, 60, (1996) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc., Rational and birational maps, Equations and inequalities involving linear operators, with vector unknowns, Transformers, preservers (linear operators on spaces of linear operators), Functional calculus for linear operators Rational operator functions and Bezoutian operator vessels | 0 |
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