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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rationally connected varieties; local fields; unirational variety; chain of rational curves J. Kollár, ''Rationally connected varieties over local fields,'' Ann. of Math., vol. 150, iss. 1, pp. 357-367, 1999. Local ground fields in algebraic geometry, Rational and unirational varieties, Group actions on varieties or schemes (quotients) Rationally connected varieties over local fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine variety; unipotent algebraic group; set of fixed points Jelonek, Z; Lasoń, M, The set of fixed points of a unipotent group, J. Algebra, 322, 2180-2185, (2009) Group actions on varieties or schemes (quotients), Linear algebraic groups over arbitrary fields The set of fixed points of a unipotent group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli stacks of curves; trigonal curves; mapping class groups; Teichmüller spaces; braid groups; orbifold fundamental group Bolognesi, M.; Lönne, M., \textit{mapping class groups of trigonal loci.}, Selecta Math. (N.S.), 22, 417-445, (2016) Families, moduli of curves (algebraic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Coverings of curves, fundamental group, Stacks and moduli problems Mapping class groups of trigonal loci
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) isomorphism classes of simple n-dimensional representation of a finitely generated group; tangents to formal curves; algebraic set; tangent cones to representation varieties DOI: 10.1007/BF02783301 Varieties and morphisms, Representation theory for linear algebraic groups, Linear algebraic groups over the reals, the complexes, the quaternions Local structure of representation varieties
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) braid group; moduli space of Riemann spheres; outer automorphisms; algebraic fundamental group; Grothendieck-Teichmüller group D. Harbater and L. Schneps: Fundamental groups of moduli and the Grothendieck--Teichmüller group , Trans. Amer. Math. Soc. 352 (2000), 3117--3148. JSTOR: Homotopy theory and fundamental groups in algebraic geometry, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Families, moduli of curves (algebraic), Fundamental groups and their automorphisms (group-theoretic aspects) Fundamental groups of moduli and the Grothendieck-Teichmüller group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weil curves; elliptic curve; L-function; Shafarevich-Tate group Борисов, А. В.; Мамаев, И. С., Странные аттракторы в динамике кельтских камней, УФН, 173, 4, 407-418, (2003) Arithmetic ground fields for curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Rational points, Quadratic extensions, Elliptic curves, Special algebraic curves and curves of low genus Finiteness of \(E({\mathbb{Q}})\) and Ш\((E,{\mathbb{Q}})\) for a subclass of Weil curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) absolute Galois group of rational function field; real closed field; Tarski principle; transfer principle L P.D. v.d. Dries and P. Ribenboim , An application of Tarski's principle to absolute Galois groups of function fields , Queen's Mathematical Preprint No. 1984-8. Separable extensions, Galois theory, Ultraproducts and field theory, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Real algebraic and real-analytic geometry An application of Tarski's principle to absolute Galois groups of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) minimal surface of general type; finite group of automorphisms Xiao G. (1990). On abelian automorphism group of a surface of general type. Invent. Math. 102(3): 619--631 Surfaces of general type, Automorphisms of surfaces and higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations On abelian automorphism group of a surface of general type
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) real algebraic curves; birational automorphisms; number of fixed points Topology of real algebraic varieties, Real algebraic sets, Automorphisms of curves Fixed points of automorphisms of real algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) generalization of class field theory; local fields; global fields; Milnor K-group; integral projective scheme; Chow group; generalization of ramification theory; higher dimensional schemes; generalized Swan conductor Kato, K. : A generalization of class field theory (Japanese) . Sûgaku 40 (1988) 289-311. 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) A generalization of class field theory
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cellular complex; complement of a family of hyperplanes in \(\mathbb{C}^ N\); homology of local systems on an affine space; homology group; configurations of hyperplanes; fundamental strata; Grassmannian Prati, M. C.; Salvetti, M.: On local system over complements to arrangements of hyperplanes associated to grassman strata. Ann. mat. Pura appl. 159, 341-355 (1991) Algebraic topology on manifolds and differential topology, Homology with local coefficients, equivariant cohomology, Special varieties On local systems over complements to arrangements of hyperplanes associated to Grassmann strata
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of points on elliptic curves; finite fields Curves over finite and local fields, Finite ground fields in algebraic geometry The number of points on elliptic curves \(E\colon y^ 2=x^ 3+cx\) over \(\mathbb F_ p\bmod 8\).
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) theta-function; tau-function; classical limit; form factors of fields; Knizhnik-Zamolodchikov equation; finite-gap integration Smirnov F.A. (1993) Form factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration. Commun. Math. Phys. 155, 459--487 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.), Theta functions and curves; Schottky problem Form factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global function fields; rational places; rational points; curves over finite fields; class field towers; applications to coding theory; low-discrepancy sequences Niederreiter, Harald; Xing, Chaoping: Rational points on curves over finite fields--theory and applications, (2000) Curves over finite and local fields, Rational points, Applications to coding theory and cryptography of arithmetic geometry, General theory of distribution modulo \(1\) Algebraic curves over finite fields with many rational points and their applications
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic genus; formal group laws associated to supersingular elliptic curves; Jacobi quartics; Legendre polynomials; elliptic curves of Weierstrass forms; discriminant Landweber, P.S.: Supersingular Elliptic Curves and Congruences for Legendre Polynomials. In: Landweber, P.S. (ed.) Elliptic Curves and Modular Forms in Topology. Proceedings, Princeton 1986. (Lect. Notes Math., vol. 1326, pp. 69--93) Berlin Heidelberg New York: Springer 1988 Formal groups, \(p\)-divisible groups, Spherical harmonics, Special algebraic curves and curves of low genus, Elliptic curves Supersingular elliptic curves and congruences for Legendre polynomials
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) modular curves; splitting of primes; number fields Arithmetic aspects of modular and Shimura varieties, Elliptic curves over global fields, Rational points Splitting of primes in number fields generated by points on some modular curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic on curves of genus one; Tate-Shafarevich group; Selmer group; Weil-Chatelet group Cassels, J. W. S., Arithmetic on curves of genus 1. III. the Tate-šafarevič and Selmer groups, Proc. London Math. Soc. (3), 12, 259-296, (1962) Curves over finite and local fields, Arithmetic ground fields for curves Arithmetic on curves of genus 1. III: The Tate-Shafarevich and Selmer groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms of an affine surface Rosay, J.-P.: Automorphisms of \({\mathbb{C}}^n\), a survey of Andersén-Lempert theory and applications, Contemp. Math., vol. 222. AMS, Providence (1999) Automorphisms of surfaces and higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations, Polynomial rings and ideals; rings of integer-valued polynomials On groups of automorphisms of a class of surfaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves and abelian varieties over finite fields; distribution of the trace of matrices; equidistribution; Frobenius operator; generalized Sato-Tate conjecture; Katz-Sarnak theory; random matrices; Weyl's integration formula Curves over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Relations with random matrices, Representations of Lie and linear algebraic groups over real fields: analytic methods, Symmetric functions and generalizations, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Random matrices (probabilistic aspects) On the distribution of the trace in the unitary symplectic group and the distribution of Frobenius
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois cohomology; number fields; elliptic curves; abelian varieties; function fields; profinite groups; class field theory; formal groups; Milnor K-groups; Lubi-Tate groups Collected or selected works; reprintings or translations of classics, History of number theory, History of algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic problems in algebraic geometry; Diophantine geometry, Abelian varieties and schemes Collected works of John Tate. Part I (1951--1975). Edited by Barry Mazur and Jean-Pierre Serre
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fixed-point-free elements in finite groups; value set of a polynomial; curves over finite fields Guralnick, R., Wan, D.: Bounds for fixed point free elements in a transitive group and applications to curves over finite fields. Isr. J. Math. 101, 255--287 (1997) Polynomials over finite fields, Curves over finite and local fields, Finite ground fields in algebraic geometry, Finite fields (field-theoretic aspects) Bounds for fixed point free elements in a transitive group and applications to curves over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of vector bundles; representation spaces; fundamental group; Seifert manifold; \({\mathbb{Z}}\)-homology sphere; Floer homology; Morse function; Dolgachev surface; Chern classes; smooth rational varieties; Betti numbers; Weil conjectures S. Bauer and C. Okonek, The algebraic geometry of representation spaces associated to Seifert fibered homology \(3\)-spheres , Math. Ann. 286 (1990), no. 1-3, 45-76. General low-dimensional topology, Special surfaces The algebraic geometry of representation spaces associated to Seifert fibered homology 3-spheres
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell's conjecture over function fields; theorem of the kernel . Coleman, R.F. , '' Manin's proof of the Mordell conjecture over function fields '', preprint. Rational points, Families, moduli of curves (algebraic), Algebraic functions and function fields in algebraic geometry Manin's proof of the Mordell conjecture over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois covers of curves; inertia group Rachel J. Pries, ``Families of wildly ramified covers of curves'', Am. J. Math.124 (2002) no. 4, p. 737-768 Coverings of curves, fundamental group, Ramification problems in algebraic geometry Families of wildly ramified covers of curves.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Schwartz-Bruhat space; complex power of a K-analytic function; desingularisation; exceptional curves J. Igusa , Complex powers of irreducible algebroid curves, in Geometry today, Roma 1984 , Progress in Mathematics 60, Birkhaüser (1985), 207-230. Arithmetic ground fields for curves, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of curves, local rings, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Local ground fields in algebraic geometry Complex powers of irreducible algebroid curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) group of automorphisms; categorical quotient of a variety; invariant of a linear group; variety of \(m\)-typles Zubkov, A.N.: Invariants of an adjoint action of classical groups. Algebra Logic 38(5), 299--318 (1999) Geometric invariant theory, Actions of groups on commutative rings; invariant theory, Group actions on varieties or schemes (quotients), Classical groups (algebro-geometric aspects), Linear algebraic groups over arbitrary fields Invariants of an adjoint action of classical groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Castelnuovo-Mumford regularity; rational points in projective spaces over finite fields; Hilbert function; index of stability E. Kunz and R. Waldi, On the regularity of configurations of \(\mathbb{F}_q\)-rational points in projective space , J. Comm. Alg. 5 (2013), 269-280. Finite ground fields in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Rational points, Finite fields and commutative rings (number-theoretic aspects) On the regularity of configurations of \(\mathbb F_q\)-rational points in projective space
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) von Neumann regular; irreducible varieties; irreducible affine algebraic monoid; group of units Renner, L. E.,Reductive monoids are von Neumann regular, J. of Algebra93 (1985), 237--245. General structure theory for semigroups, Semigroups of transformations, relations, partitions, etc., Linear algebraic groups and related topics, Generalizations (algebraic spaces, stacks) Reductive monoids are von Neumann regular
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field analogue of the theory of elliptic modular curves; Drinfeld modules; Drinfeld's upper half-plane; expansions at the cusps of certain modular forms; Manin-Drinfeld theorem; algebraic modular forms; jacobian Ernst-Ulrich Gekeler, Drinfel\(^{\prime}\)d modular curves, Lecture Notes in Mathematics, vol. 1231, Springer-Verlag, Berlin, 1986. Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for curves, Modular forms associated to Drinfel'd modules, Global ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic theory of algebraic function fields Drinfeld modular curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois group; general linear group; algebraic fundamental group; unramified covering of the affine line; general semilinear group Abhyankar S S, Semilinear transformations,Proc. Am. Math. Soc. 127 (1999) 2511--2525 Separable extensions, Galois theory, Coverings of curves, fundamental group Semilinear transformations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Coxeter group; two sided cells; affine Weyl group; unipotent classes; complex reductive group; variety of Borel subgroups; affine Hecke algebras; equivariant vector bundles Lusztig, G., Cells in affine Weyl groups, IV, \textit{J. Fac. Sci. Univ. Tokyo Sect. IA. Math.}, 36, 297-328, (1989) Representation theory for linear algebraic groups, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Cells in affine Weyl groups. IV
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) generating function; Belyi functions; algebraic curves; automorphism group; fatgraphs Di Francesco, P.; Itzykson, C., A generating function for fatgraphs, Ann. Inst. Henri Poincaré Phys. Théor., 59, 117-139, (1993) Enumeration in graph theory, Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group, Representations of finite symmetric groups, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry A generating function for fatgraphs
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Siegel modular group; resolution of cusps; rational Hilbert modular surfaces; canonical maps; modular curves; intersection theory; moduli spaces; abelian varieties with real multiplication; Kummer surface Friedrich Hirzebruch and Gerard van der Geer, Lectures on Hilbert modular surfaces, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 77, Presses de l'Université de Montréal, Montreal, Que., 1981. Based on notes taken by W. Hausmann and F. J. Koll. Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Modular and Shimura varieties, Singularities of surfaces or higher-dimensional varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic ground fields for surfaces or higher-dimensional varieties, Families, moduli, classification: algebraic theory, Algebraic moduli of abelian varieties, classification, Abelian varieties and schemes, Global theory and resolution of singularities (algebro-geometric aspects) Lectures on Hilbert modular surfaces. Notes by W. Hausmann and F. J. Koll
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli problem; integrble systems; generic affine variety; flows of the integrable vector fields; geodesic flow Bueken, P. and Vanhaecke, P., The Moduli Problem for Integrable Systems: The Example of a Geodesic Flow on SO(4), J. London Math. Soc. (2), 2000, vol. 62, no. 2, pp. 357--369. Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Geodesic flows in symplectic geometry and contact geometry, Relationships between algebraic curves and integrable systems, Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.), Algebraic moduli of abelian varieties, classification, Jacobians, Prym varieties The moduli problem for integrable systems: the example of a geodesic flow on SO(4)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism groups of function fields; function fields over finite fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Automorphisms of curves, Applications to coding theory and cryptography of arithmetic geometry The asymptotic behavior of automorphism groups of function fields over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell-Weil groups; elliptic curves; function fields; fibrations Algebraic functions and function fields in algebraic geometry, Rational points, Fibrations, degenerations in algebraic geometry, Elliptic curves On Shioda's Mordell-Weil lattices of higher genus fibrations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cuspidal divisor class group; group of modular units; modular; curves; congruence subgroups; Jacobian; cuspidal groups; arithmetic of special values of L-functions; weight two Eisenstein series; congruence formulae Glenn Stevens, The cuspidal group and special values of \(L\)-functions, Trans. Am. Math. Soc.291 (1985), p. 519-550 Holomorphic modular forms of integral weight, Congruences for modular and \(p\)-adic modular forms, Jacobians, Prym varieties The cuspidal group and special values of L-functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) effective Chabauty; cardinality of rational points on a curve; Fermat's Last Theorem; rank of the Mordell-Weil group; Fermat curve; rational points on curves W. G. McCallum, ''On the method of Coleman and Chabauty,'' Math. Ann., vol. 299, iss. 3, pp. 565-596, 1994. Rational points, Arithmetic ground fields for curves, Higher degree equations; Fermat's equation On the method of Coleman and Chabauty
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) connected Lie group; affine transformations; complex affine plane; finite number of orbits; orbital decompositions Other geometric groups, including crystallographic groups, Noncompact Lie groups of transformations, Geometry of classical groups, Group actions on varieties or schemes (quotients) Finite orbital decompositions for groups of affine transformations of the plane
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) projective curves of genus \(g\) with \(n\)-marked points; pro-\(l\) towers of fields of definition; moduli stack; Galois-Teichmüller modular groups; nonabelian analogs of the Tate conjecture Hiroaki Nakamura, Coupling of universal monodromy representations of Galois-Teichmüller modular groups, Math. Ann. 304 (1996), no. 1, 99 -- 119. Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Other groups and their modular and automorphic forms (several variables) Coupling of universal monodromy representations of Galois-Teichmüller modular groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Discriminants; polar curves; to vanish; double root; triple root; differential coefficient; function of several variables; homogeneous coordinates; pole of a curve; order; double points; locus; peak; tangent Algebraic functions and function fields in algebraic geometry, Plane and space curves, Real polynomials: location of zeros, Continuity and differentiation questions, Curves in Euclidean and related spaces, Steiner systems in finite geometry On certain formulae concerning the theory of discriminants; with applications to discriminants of discriminants, and to the theory of polar curves.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) galois automorphisms; fundamental group of the projective line minus three points Coverings of curves, fundamental group, Galois theory, Global ground fields in algebraic geometry, Coverings in algebraic geometry On galois automorphisms of the fundamental group of the projective line minus three points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) field of definition of the Néron-Severi group; 2-coverings; elliptic curve over function field H.P.F. Swinnerton-Dyer , The field of definition of the Néron-Severi group , Studies in Pure Mathematics, 719-731. Rational points, Special algebraic curves and curves of low genus, Elliptic curves The field of definition of the Néron-Severi group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) gonality; hyperbolic volume; first eigenvalue; Laplacian; non-Archimedean field; rigid analytic; graphs; stable gonality; harmonic morphism; Drinfeld modular curves; congruence subgroups function fields Cornelissen, G.; Kato, F.; Kool, J., \textit{A combinatorial Li-Yau inequality and rational points on curves}, Math. Ann., 361, 211-256, (2015) Drinfel'd modules; higher-dimensional motives, etc., Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Graphs and linear algebra (matrices, eigenvalues, etc.), Rational points, Rigid analytic geometry, Special divisors on curves (gonality, Brill-Noether theory) A combinatorial Li-Yau inequality and rational points on curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) lifting problem; deformation of \({\mathbb{G}}_ a\) to \({\mathbb{G}}_ m\); characteristic p; automorphism group; Galois covering of curves; class field theory; Artin-Schreier sequence; Kummer sequence Sekiguchi, T.; Oort, F.; Suwa, N., On the deformation of Artin-Schreier to Kummer, Annales Scientifiques de l'École Normale Supérieure, 22, 345-375, (1989) Coverings of curves, fundamental group, Birational automorphisms, Cremona group and generalizations, Class field theory; \(p\)-adic formal groups On the deformation of Artin-Schreier to Kummer
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms of polynomial algebras; affine spaces; homogeneous system of parameters; Gröbner bases Furter, J-P, Polynomial composition rigidity and plane polynomial automorphisms, J. Lond. Math. Soc., 91, 180-202, (2015) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Computational aspects and applications of commutative rings, Actions of groups on commutative rings; invariant theory, Polynomials over commutative rings Polynomial composition rigidity and plane polynomial automorphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) solvable fundamental group; Veronese surfaces; complement of branch curves; solvable groups; Veronese embedding Teicher M. The fundamental group of a \(\mathbb{C}\)\(\mathbb{P}\)2 complement of a branch curve as an extension of a solvable group by a symmetric group. Math Ann, 314: 19--38 (1999) Homotopy theory and fundamental groups in algebraic geometry, Solvable groups, supersolvable groups, Coverings of curves, fundamental group The fundamental group of a \(\mathbb{C}\mathbb{P}^2\) complement of a branch curve as an extension of a solvable group by a symmetric group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) extension of ground fields; elliptic fibration; elliptic surface; function field; conjectures of Birch and Swinnerton-Dyer G. R. Grant and E. Manduchi, Root numbers and algebraic points on elliptic surfaces with base \(\mathbbP^1\) , Duke Math. J. 89 (1997), no. 3, 413-422. Rational points, Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Root numbers and algebraic points on elliptic surfaces with base \(\mathbb{P}^1\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic \(F\)-representations; retract rational extensions; stably isomorphic extensions; lifting property; Azumaya algebras; fields of invariants; rational function fields; generic division algebras; central simple algebras D. J. Saltman, J.-P. Tignol, Generic algebras with involution of degree 8m, J. Algebra 258 (2002), no. 2, 535--542. Finite-dimensional division rings, Rings with involution; Lie, Jordan and other nonassociative structures, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Geometric invariant theory Generic algebras with involution of degree \(8m\).
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Azumaya algebras; Brauer groups; Brauer-Manin obstructions; Hasse principle; quartic curves; curves of genus 1; Tate-Shafarevich group DOI: 10.1007/s00605-012-0387-8 Rational points, Varieties over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields The arithmetic of certain quartic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic function fields; imaginary quadratic function field; real quadratic function field; divisor class group; reduced ideals; group law [14]S. Paulus and H.-G. Rück, Real and imaginary quadratic representations of hyperelliptic function fields, Math. Comput. 68 (1999), 1233--1241. Arithmetic theory of algebraic function fields, Class groups and Picard groups of orders, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry Real and imaginary quadratic representations of hyperelliptic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) trivial Mordell-Weil group; elliptic curve; order of the 3-primary component of the ideal class group of quadratic fields J. Nakagawa and K. Horie: Elliptic curves with no rational points. Proc. A.M.S., 104, 20-24 (1988). JSTOR: Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Quadratic extensions, Density theorems, Global ground fields in algebraic geometry Elliptic curves with no rational points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves over finite fields with many rational points; asymptotic lower bounds; class field towers; degree-2 covering of curves Elkies, ND; Howe, EW; Kresch, A; Poonen, B; Wetherell, JL; Zieve, ME, \textit{curves of every genus with many points}, II\textit{: asymptotically good families}, Duke Math. J., 122, 399-422, (2004) Curves over finite and local fields, Rational points, Finite ground fields in algebraic geometry Curves of every genus with many points. II: Asymptotically good families
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli of compact Riemann surfaces of a given genus; surfaces with automorphisms; Fuchsian groups; topological and conformal conjugacy of group actions on surfaces; Teichmüller space Weaver, A.: Stratifying the space of moduli. Teichmüller theory and moduli problem, pp. 597-618. In: Ramanujan Mathematical Society Lecture Notes Series, vol. 10. Ramanujan Mathematical Society, Mysore (2010) Vector bundles on curves and their moduli, Families, moduli of curves (analytic), Compact Riemann surfaces and uniformization, Conformal metrics (hyperbolic, Poincaré, distance functions), Teichmüller theory for Riemann surfaces Stratifying the space of moduli
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Cremona group; birational map; automorphisms of surfaces Automorphisms of surfaces and higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations On regularizable birational maps
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) stably rational homogeneous space; group scheme; embedding; group of automorphisms A. Schofield, ''Matrix invariants of composite size,'' Preprint (1989). Homogeneous spaces and generalizations, Rational and birational maps Matrix invariants of composite size
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) sum of divisors function; symmetric group; permutation John R. Britnell, A formal identity involving commuting triples of permutations, J. Combin. Theory Ser. A 120 (2013), no. 4, 941 -- 943. Arithmetic functions; related numbers; inversion formulas, Permutations, words, matrices, Special sequences and polynomials, Coverings of curves, fundamental group A formal identity involving commuting triples of permutations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) PAC fields; function field; Tate-Shafarevich group; stably birational invariant; flasque resolution Varieties over global fields, Birational geometry, Brauer groups of schemes On the character with stably birational invariant of a Tate-Shafarevich group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Kummer surface; Brauer group; rational points; torsion of elliptic curves A.N. Skorobogatov, Yu.G. Zarhin, The Brauer group of Kummer surfaces and torsion of elliptic curves, J. Reine Angew. Math. 666, 115-140 (2012) \(K3\) surfaces and Enriques surfaces, Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties The Brauer group of Kummer surfaces and torsion of elliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic number theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. Research exposition (monographs, survey articles) pertaining to number theory, Class field theory, Class field theory; \(p\)-adic formal groups, Ramification and extension theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Collected or selected works; reprintings or translations of classics Algebraic numbers and algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Dirichlet \(L\)-functions; moments of \(L\)-functions; function fields; finite fields; random matrix theory Zeta and \(L\)-functions in characteristic \(p\), Polynomials over finite fields, Relations with random matrices, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of polynomial rings over finite fields The integrated fourth moment of Dirichlet \(L\)-functions over rational function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic-geometry codes; towers of function fields; \(Q\)th-power map Leonard, D. A.: Finding the missing functions for one-point AG codes. IEEE trans. Inform. theory 47, No. 6, 2566-2573 (2001) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic theory of algebraic function fields Finding the defining functions for one-point algebraic-geometry codes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) partially ordered sets; finite representation type; irreducible affine varieties; bipartitioned matrices; group actions; degenerations of orbits; prinjective modules; incidence algebras; Tits quadratic forms Kosakowska, J.: Degenerations in a class of matrix varieties and prinjective modules. J. Algebra 263, 262--277 (2003) Representations of quivers and partially ordered sets, Group actions on varieties or schemes (quotients), Ext and Tor, generalizations, Künneth formula (category-theoretic aspects), Group actions on affine varieties, Canonical forms, reductions, classification, Multilinear algebra, tensor calculus Degenerations in a class of matrix varieties and prinjective modules
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) representations; D-modules; flag manifolds; affine Weyl group; sheaf of twisted differential operators Tanisaki, T.: Twisted differential operators and affine Weyl groups. J. fac. Sci. univ. Tokyo sect. IA math. 34, No. 2, 203-221 (1987) Semisimple Lie groups and their representations, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Affine algebraic groups, hyperalgebra constructions, Cohomology theory for linear algebraic groups Twisted differential operators and affine Weyl groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) towers of algebraic function fields; genus; number of places Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Finite ground fields in algebraic geometry On a tower of Garcia and Stichtenoth
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) bilinear complexity; congruence function fields; descent of function fields; tensor rank; finite fields; Artin--Schreier extensions Ballet, Stéphane; Le Brigand, Dominique; Rolland, Robert, On an application of the definition field descent of a tower of function fields.Arithmetics, geometry, and coding theory (AGCT 2005), Sémin. Congr. 21, 187-203, (2010), Soc. Math. France, Paris Number-theoretic algorithms; complexity, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves On an application of the definition field descent of a tower of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) real Schubert calculus; Wronski map; rational normal curves; characters of the symmetric group Grassmannians, Schubert varieties, flag manifolds, Classical problems, Schubert calculus, Real algebraic sets A topological proof of the Shapiro-Shapiro conjecture
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rank of elliptic curves; theorem of Lutz-Nagel; \(2\)-descent; families of elliptic curves; arithmetic function; quartic diophantine equation Elliptic curves over global fields, Other results on the distribution of values or the characterization of arithmetic functions, Elliptic curves Families of elliptic curves of rank \(\geq 1\) and remarks on an arithmetic function associated to an algorithm of 2-descent of Tate
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) group of birational automorphisms F. Catanese and M. Schneider, ''Polynomial bounds for abelian groups of automorphisms,'' Compositio Math., vol. 97, iss. 1-2, pp. 1-15, 1995. Automorphisms of curves, Group actions on varieties or schemes (quotients) Polynomial bounds for abelian groups of automorphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hilbert modular variety; unit with negative norm; cyclotomic fields; cyclic fields; Hilbert modular group; arithmetical genus; number of elliptic fixed points; class number; totally real fields Keqin, F.: On arithmetic genus of Hilbert modular varieties on cyclic number fields. Sci. China 27, 576-584 (1984) Totally real fields, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Cyclotomic extensions, Units and factorization, Iwasawa theory, Arithmetic ground fields for surfaces or higher-dimensional varieties On the arithmetic genus of Hilbert modular varieties over cyclic number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) valued function fields; good reduction; regular functions; reciprocity lemma; unit; local symbols; local-global principle; solvability of diophantine equations P. Roquette, \textsl Reciprocity in valued function fields, Journal für die reine und angewandte Mathematik 375/376 (1987), 238--258. Arithmetic theory of algebraic function fields, Valued fields, Algebraic functions and function fields in algebraic geometry, Diophantine equations Reciprocity in valued function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) transcendental field extensions; Galois group; elliptic function fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Transcendental field extensions, Galois theory Un exemple de groupe de Galois d'une extension transcendante
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) tautological ring; moduli of curves; stable quotients; Faber conjecture; generating function Families, moduli of curves (algebraic), Exact enumeration problems, generating functions Note on the relations in the tautological ring of \(\mathcal M_{g}\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Betti number of an abelian covering of a \(CW\)-complex; cyclotomic coordinates; fundamental group; complement to an algebraic curve; link; Alexander polynomials of plane algebraic curves Libgober A.: On the homology of finite abelian coverings. Topol. Appl. 43(2), 157--166 (1992) Coverings in algebraic geometry, Fundamental group, presentations, free differential calculus, Homotopy theory and fundamental groups in algebraic geometry, Coverings of curves, fundamental group, Covering spaces and low-dimensional topology On the homology of finite abelian coverings
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) self-intersection of dualizing sheaves; elliptic curves; Arakelov theory; Arakelov-Green function; Frey curves; genus; Néron-Tate height; Jacobian Szpiro, L. 1990.Sur les propriétés numériques du dualisant relatif d'une surface arithmétique, The Grothendieck Festschrift Vol. III, 229--246. Boston: Birkhäuser. Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Sur les propriétés numériques du dualisant relatif d'une surface arithmétique. (On the numerical properties of the relative dualizing sheaf of an arithmetic surface)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) patching; local-global principle; two-dimensional complete domain; function field of a curve; quadratic form; Witt ring; \(u\)-invariant; Brauer group; period-index problem Harbater, D.; Hartmann, J.; Krashen, D., \textit{refinements to patching and applications to field invariants}, Int. Math. Res. Not. IMRN, 2015, 10399-10450, (2015) Algebraic functions and function fields in algebraic geometry, Brauer groups of schemes, Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Formal power series rings, Arithmetic ground fields for curves, Finite-dimensional division rings, Brauer groups (algebraic aspects), Valued fields Refinements to patching and applications to field invariants
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Coxeter group of reflections; discrete group; automorphism groups of complex spaces; signature; Galois covering; projective space; affine space; complex ball V. P. Kostov, ''Versal deformations of differential forms of degree {\(\alpha\)} on the line,'' Funkts. Anal. Prilozhen.,18, No. 4, 81--82 (1984). Complex Lie groups, group actions on complex spaces, Reflection groups, reflection geometries, Other geometric groups, including crystallographic groups, Geometries with algebraic manifold structure, Coverings in algebraic geometry, Group actions on varieties or schemes (quotients) Discrete groups of reflections in the complex ball
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite-dimensional associative algebras; affine group schemes; automorphism groups; inner automorphisms Group schemes, Group rings of finite groups and their modules (group-theoretic aspects), Automorphisms and endomorphisms Non-reduced automorphism schemes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite Tate-Shafarevich group; elliptic curves; evidence for the truth of the Birch and Swinnerton-Dyer conjecture; ideal class annihilators Rubin, K.: Tate-Shafarevich groups and
\[
L
\]
-functions of elliptic curves with complex multiplication. Invent. Math. 89, 527--560 (1987) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Complex multiplication and abelian varieties, Special algebraic curves and curves of low genus, Rational points, Elliptic curves Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weil-Deligne group; local Euler factors; L-function of motif; non-archimedean places; Tannakian category; admissible objects; Deligne motives; Dirichlet series; Riemann zeta function Deninger, C., Local \textit{L}-factors of motives and regularized determinants, Invent. Math., 107, 135-150, (1992) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Generalizations (algebraic spaces, stacks), Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Zeta and \(L\)-functions in characteristic \(p\) Local \(L\)-factors of motives and regularized determinants
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) roots of the \(L\)-functions; algebraic curves over finite fields Emmanuel Kowalski, The principle of the large sieve, available at arXiv:math.NT/0610021. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Other Dirichlet series and zeta functions, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Curves over finite and local fields, Relations with random matrices, Applications of sieve methods The large sieve, monodromy, and zeta functions of algebraic curves. II: Independence of the zeros
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves in projective spaces; lines; Hilbert function; union of lines Plane and space curves, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series On the Hilbert function of intersections of a hypersurface with general reducible curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) perverse coherent sheaves; special pieces in unipotent varieties; Macaulayfication; schemes of finite type; affine group schemes; intersection cohomology functors Achar, P; Sage, D, Perverse coherent sheaves and the geometry of special pieces in the unipotent variety, Adv. Math., 220, 1265-1296, (2009) Representation theory for linear algebraic groups, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Group schemes, Cohomology theory for linear algebraic groups Perverse coherent sheaves and the geometry of special pieces in the unipotent variety.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic theory of algebraic function fields; towers of function fields; Zink's bound; Hasse-Witt invariant; \(p\)-rank [2]A. Bassa and P. Beelen, The Hasse--Witt invariant in some towers of function fields over finite fields, Bull. Brazil. Math. Soc. 41 (2010), 567--582. Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry The Hasse-Witt invariant in some towers of function fields over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) simple affine contractions; classification of birational endomorphisms; missing curves Daigle D., J. Math. Kyoto Univ. 31 pp 329-- (1991) Rational and birational maps Birational endomorphisms of the affine plane
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fields of moduli of curves; field of definition Dèbes, P.; Emsalem, M., On fields of moduli of curves, J. Algebra, 211, 42-56, (1999) Families, moduli of curves (algebraic), Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Coverings of curves, fundamental group On fields of moduli of curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) isotropy; local-global principle; real field; sums of squares; \(u\)-invariant; pythagoras number; valuation; algebraic function fields Becher, Karim; Grimm, David; Van Geel, Jan: Sums of squares in algebraic function fields over a complete discretely valued field, Pacific J. Math. 267, No. 2, 257-276 (2014) Quadratic forms over general fields, Forms over real fields, Sums of squares and representations by other particular quadratic forms, Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Transcendental field extensions, Algebraic functions and function fields in algebraic geometry Sums of squares in algebraic function fields over a complete discretely valued field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) family of curves; large monodromy; finite ground field; numerator of the zeta function; Katz's conjecture Chavdarov, N., \textit{the generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy}, Duke Math. J., 87, 151-180, (1997) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture The generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Witt ring; fundamental ideal; bilinear forms; curves over local fields; Brauer group Local ground fields in algebraic geometry, Algebraic theory of quadratic forms; Witt groups and rings, Curves over finite and local fields, Arithmetic ground fields for curves The Witt ring of a curve with good reduction over a non-dyadic local field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of rational points; curves defined over finite fields; Frobenius map; degrees; dual curves Hefez, Abramo; Voloch, José Felipe: Frobenius nonclassical curves. Arch. math. (Basel) 54, No. 3, 263-273 (1990) Arithmetic ground fields for curves, Finite ground fields in algebraic geometry, Rational points Frobenius non classical curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(L\)-functions; function fields for hyperelliptic curves Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Algebraic functions and function fields in algebraic geometry Note on explicit formulas of \(L\)-functions of some hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine space; affine Cremona group; affine group; closed subgroups; transitive group action; linear automorphisms Bodnarchuk, Y, Some extreme properties of the affine group as an automorphisms group of the affine space, Contribution to General Algebra, 13, 15-29, (2001) Birational automorphisms, Cremona group and generalizations, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Linear algebraic groups over arbitrary fields Some extreme properties of the affine group as an automophism group of the affine space
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli spaces of curves; algebraic curves over global fields; discriminantal varieties; cohomology rings; Hodge structures Bergstrom, J.; Tommasi, O., The rational cohomology of M\_{}\{4\}, Math. Ann., 338, 207, (2007) Families, moduli of curves (algebraic), Curves over finite and local fields, Discriminantal varieties and configuration spaces in algebraic topology, Arithmetic ground fields for curves, Transcendental methods, Hodge theory (algebro-geometric aspects), Topological properties in algebraic geometry The rational cohomology of \(\overline{\mathcal{M}}_4\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Siegel modular group; Siegel modular function field; seven generators of \(K_ 3\) Theta series; Weil representation; theta correspondences, Global ground fields in algebraic geometry On the Siegel modular function field of degree three
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) construction of high-rank elliptic curves; Mordell-Weil group K. Nagao, Construction of high-rank elliptic curves, Kobe J. Math,11 (1994), 211--219. Elliptic curves over global fields, Elliptic curves Construction of high-rank elliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Jacobian; determinantal variety; curve without automorphisms; automorphism group of the moduli space Kouvidakis, A., and Pantev, T., \textit{The automorphism group of the moduli space of semistable}\textit{vector bundles}, Math. Ann. 302 (1995), no. 2, 225--268. Vector bundles on curves and their moduli, Automorphisms of curves, Algebraic moduli problems, moduli of vector bundles The automorphism group of the moduli space of semi stable vector bundles
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of curves; mapping class group; level structures; Picard group; Torelli group; group cohomology Ivanov, N. V.: Subgroups of Teichmüller modular groups. Translations of Mathematical Monographs \textbf{115}. AMS (1992) Families, moduli of curves (algebraic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Picard groups, General geometric structures on low-dimensional manifolds The second rational homology group of the moduli space of curves with level structures
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) height function; elliptic curves over function fields; specialization map Elliptic curves over global fields, Heights, Arithmetic varieties and schemes; Arakelov theory; heights Heights and the specialization map for families of elliptic curves over \(\mathbb {P}^n\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine surfaces; algebraic action of the additive group of complex numbers; equivariant compactifications; singular homology Fieseler, K-H, On complex affine surfaces with \({\mathbb{C}}^+\)-action, Comment. Math. Helv., 69, 5-27, (1994) Group actions on varieties or schemes (quotients), Compactification of analytic spaces, Surfaces and higher-dimensional varieties On complex affine surfaces with \(\mathbb{C}^ +\)-action
| 0 |
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