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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 \(x^n+y^m+1=0\) Teichmüller modular function fields; pro-\(l\) number field towers; moduli stack of smooth projective curves; stability; braid groups Nakamura, H.; Takao, N.; Ueno, R., Some stability properties of Teichmüller modular function fields with pro-\textit{} weight structures, Math. ann., 302, 197-213, (1995), MR 96h:14041 Arithmetic ground fields for curves, Coverings of curves, fundamental group, Families, moduli of curves (algebraic), Braid groups; Artin groups Some stability properties of Teichmüller modular function fields with pro-\(l\) weight 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 \(x^n+y^m+1=0\) action of affine algebraic group; algebra automorphisms; minimal injective resolutions Magid, A, Cohomology of rings with algebraic group action, Adv. Math., 59, 124-151, (1986) Group actions on varieties or schemes (quotients), Homological dimension and commutative rings, Injective and flat modules and ideals in commutative rings Cohomology of rings with algebraic group action
| 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 fields; irreducible polynomials; hyperelliptic curves; derivatives of \(L\)-functions; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory Zeta and \(L\)-functions in characteristic \(p\), \(\zeta (s)\) and \(L(s, \chi)\), Curves over finite and local fields, Relations with random matrices, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Mean values of derivatives of \(L\)-functions in function fields. III
| 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 curves over function fields; explicit computation of \(L\)-functions; special values of \(L\)-functions and BSD conjecture; estimates of special values; analogue of the Brauer-Siegel theorem Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Zeta and \(L\)-functions in characteristic \(p\) Explicit \(L\)-functions and a Brauer-Siegel theorem for Hessian 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 \(x^n+y^m+1=0\) singular cubics; isogenies; torsion points; elliptic curves over finite fields; elliptic curves over local fields; Selmer groups; duality; rational torsion; heights; complex multiplication; integral points; Galois representations; survey; group law; endomorphism ring; Weil pairing; elliptic functions; formal group; Shafarevich-Tate groups; \(L\)-series; Tate curves; descent; conjecture of Birch and Swinnerton-Dyer Silverman, J. H.: A survey of the arithmetic theory of elliptic curves. Modular forms and Fermat's last theorem (1997) Elliptic curves over global fields, Elliptic curves over local fields, Research exposition (monographs, survey articles) pertaining to number theory, Elliptic curves, Complex multiplication and moduli of abelian varieties, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Rational points A survey of the arithmetic theory 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 \(x^n+y^m+1=0\) quadratic forms; \(u\)-invariant; power series fields; function fields of curves; orderings of fields; patching of fields Scheiderer, Claus: The u-invariant of one-dimensional function fields over real power series fields, Arch. math. (Basel) 93, No. 3, 245-251 (2009) Algebraic theory of quadratic forms; Witt groups and rings, Quadratic forms over general fields, Algebraic functions and function fields in algebraic geometry The \(u\)-invariant of one-dimensional function fields over real power series 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 \(x^n+y^m+1=0\) coverings of curves; projective curve; automorphism group; linear fractional transformation; algebraic function field; finite Galois extension; Galois group Arithmetic theory of algebraic function fields, Coverings in algebraic geometry, Galois theory Galois groups acting as linear fractional 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 \(x^n+y^m+1=0\) elliptic curves; number fields; torsion group; abelian 2-extensions of \(\mathbb{Q}\); \(K\)-isogeny class Elliptic curves, Elliptic curves over global fields Torsion of elliptic curves over 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 \(x^n+y^m+1=0\) algebraic function fields; finite field of constants; Severi's algebraic theory of correspondences; Hurwitz's transcendental theory; group of divisor classes; Riemann hypothesis for function fields; action of Galois group André Weil, Sur les fonctions algébriques à corps de constantes fini, C. R. Acad. Sci. Paris 210 (1940), 592 -- 594 (French). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry Sur les fonctions algébriques à corps de constantes fini
| 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 \(x^n+y^m+1=0\) Brauer groups; indecomposable division algebras; noncrossed products; ramification; function fields of smooth curves; non-crossed product central division algebras; exponents; indices; periods; tensor products of central algebras E. Brussel, K. McKinnie, and E. Tengan, Indecomposable and noncrossed product division algebras over function fields of smooth \?-adic curves, Adv. Math. 226 (2011), no. 5, 4316 -- 4337. Finite-dimensional division rings, Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Brauer groups (algebraic aspects) Indecomposable and noncrossed product division algebras over function fields of smooth \(p\)-adic 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 \(x^n+y^m+1=0\) Mordell-Weil group; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear. Algebraic functions and function fields in algebraic geometry, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields Constructing curves with high rank via symmetry
| 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 geometric Bogomolov conjecture; curves of genus 3 over function fields; self-intersection of the relative dualizing sheaf; admissible constants of the metrized dual graph K. Yamaki, Geometric Bogomolov's conjecture for curves of genus 3 over function fields, J. Math. Kyoto Univ. 42 (2002), 57-81. Varieties over global fields, Global ground fields in algebraic geometry Geometric Bogomolov's conjecture for curves of genus 3 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 \(x^n+y^m+1=0\) division algebras; cyclic algebras; ramifications; étale cohomology; function fields of surfaces; affine schemes; Brauer groups; central algebras; fields of fractions; cyclic Galois extensions Colliot-Thélène, J.-L.: Conjectures de type local-global sur image des groupes de Chow dans la cohomologie étale. In: Algebraic K-theory (Seattle, WA, 1997), Proceedings of Symposia in Pure Mathematics, vol. 67, pp. 1-12. Amer. Math. Soc., Providence (1999) Finite-dimensional division rings, Étale and other Grothendieck topologies and (co)homologies, Brauer groups of schemes, Brauer groups (algebraic aspects) Division algebras over 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 \(x^n+y^m+1=0\) rational points; inseparable extensions of function field; Mordell conjecture for number fields; genus drop; prime characteristic; non-conservative curves Voloch, J. F.: A Diophantine problem on algebraic curves over function fields of positive characteristic. Bull. soc. Math. France 119, 121-126 (1991) Rational points, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry, Curves in algebraic geometry A Diophantine problem on algebraic curves over function fields of positive 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 \(x^n+y^m+1=0\) genus \(\neq 1\); hyperelliptic involution; group of automorphisms of a curve; elliptic curves; isogenies; many rational points; algebraic curve; families of curves Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Algebraic curves of genus \(\geq 2\) having numerous 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 \(x^n+y^m+1=0\) p-adic L-functions; CM fields; totally complex quadratic extension of a totally real field; Grössencharacter; p-adic measure; p-adic interpolation of Hecke L-function; functional equation; non-analytic Eisenstein series; Hilbert modular group; p-adic differential operators; p-adic Eisenstein series N.M. Katz, ''p-Adic L-functions for CM-fields,'' Invent. Math. 49(3), 199--297 (1978). Zeta functions and \(L\)-functions, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), \(p\)-adic differential equations, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Complex multiplication and moduli of abelian varieties \(p\)-adic \(L\)-functions for CM 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 \(x^n+y^m+1=0\) motives; review of Iwasawa main conjecture; cyclotomic fields; elliptic curves; Selmer group; cyclotomic deformations of motives R. Greenberg, ''Iwasawa theory and \(p\)-adic deformations of motives,'' in Motives, II (Seattle, WA, 1991), Proc. Sympos. Pure Math. 55, Amer. Math. Soc., Providence, 1994, 193--223. Iwasawa theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Generalizations (algebraic spaces, stacks), Research exposition (monographs, survey articles) pertaining to number theory Iwasawa theory and \(p\)-adic deformations of motives
| 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 \(x^n+y^m+1=0\) thetanulls of cyclic curves; the group of automorphisms branch points of the projection; hyperelliptic curves Previato, E; Shaska, T; Wijesiri, GS, Thetanulls of cyclic curves of small genus, Albanian J. Math., 1, 253-270, (2007) Coverings of curves, fundamental group, Automorphisms of curves, Theta functions and abelian varieties, Theta functions and curves; Schottky problem, Special algebraic curves and curves of low genus Thetanulls of curves of small genus with 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 \(x^n+y^m+1=0\) \(L\)-series of number fields; infinite-dimensional analogue of one- parameter group; Artin formalism; self-adjoint operator; associated heat kernel; characteristic kernel; trace; asymptotic expansion; regularized determinant of the Laplacian; Selberg zeta function; theta functions J. Jorgenson, S. Lang, Artin formalism and heat kernels. Jour. Reine. Angew. Math. 447 (1994), 165-280. Zbl0789.11055 MR1263173 Other Dirichlet series and zeta functions, Spectral theory; trace formulas (e.g., that of Selberg), Heat and other parabolic equation methods for PDEs on manifolds, Theta functions and curves; Schottky problem, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Zeta functions and \(L\)-functions of number fields, Theta functions and abelian varieties Artin formalism and heat kernels
| 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 curves over function fields; Tate-Shafarevich groups; explicit computation of \(L\)-functions; BSD conjecture; Gauss and Kloosterman sums Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Gauss and Kloosterman sums; generalizations Elliptic curves with large Tate-Shafarevich groups over \(\mathbb{F}_q(t)\)
| 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 \(x^n+y^m+1=0\) Iwasawa theory; supersingular reduction; Tate-Shafarevich group; p-adic L-function; Selmer groups; ring of norms; p-adic heights; supersingular elliptic curves Perrin-Riou, Bernadette, Theorie d'Iwasawa \textit{p}-adique locale et globale, Invent. Math., 99, 247-292, (1990) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Elliptic curves Théorie d'Iwasawa p-adique locale et globale. (Local and global p-adic Iwasawa 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 \(x^n+y^m+1=0\) translations of classics (algebraic geometry); history of algebraic geometry; mathematics of the 19th century; algebraic functions; function fields; algebraic curves; Riemann-Roch theorem; algebraic differential 2.R. Dedekind, H. Weber, \(Theory of algebraic functions of one variable.\) Translated from the 1882 German original and with an introduction, bibliography and index by John Stillwell. History of Mathematics, 39. American Mathematical Society (Providence, RI; London Mathematical Society, London, 2012), pp. viii+152 History of algebraic geometry, Biographies, obituaries, personalia, bibliographies, Algebraic functions and function fields in algebraic geometry, History of mathematics in the 19th century, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Theory of algebraic functions of one variable. Transl. from the German and introduced by John Stillwell
| 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 theorem of algebraic function fields; L-function of Galois covering of curves; function-field; characteristic polynomial of the Hasse-Witt matrix; generalised Hasse-Witt invariants Cyclotomic function fields (class groups, Bernoulli objects, etc.), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Galois theory Class groups and \(L\)-series of congruence 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 coverings of curves; group of automorphisms; genus of the quotient curve; Hasse-Witt invariants Kani, E. Relations between the genera and between the Hasse-Witt invariants of Galois coverings of curves. Canad. Math. Bull.28 (3), 321--327 (1985) Coverings of curves, fundamental group, Group actions on varieties or schemes (quotients), Arithmetic ground fields for curves Relations between the genera and between the Hasse-Witt invariants of Galois coverings 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 \(x^n+y^m+1=0\) representation theory of finite-dimensional algebras; tame hereditary algebras; tame bimodules; noncommutative curves of genus zero; noncommutative function fields of genus zero D. Kussin, Parameter curves for the regular representations of tame bimodules, J. Algebra, 320 (2008), no. 6, 2567--2582.Zbl 1197.16017 MR 2437515 Representations of associative Artinian rings, Noncommutative algebraic geometry, Special algebraic curves and curves of low genus, Rings arising from noncommutative algebraic geometry, Representation type (finite, tame, wild, etc.) of associative algebras Parameter curves for the regular representations of tame bimodules.
| 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 fields; function fields; hyperelliptic curves; \(K\)-groups; moments of quadratic Dirichlet \(L\)-functions; class number Andrade, J. C.; Bae, S.; Jung, H., Average values of \textit{L}-series for real characters in function fields, Res. Math. Sci., 3, (2016), 47 Curves over finite and local fields, Zeta and \(L\)-functions in characteristic \(p\), Relations with random matrices, Arithmetic theory of algebraic function fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Average values of \(L\)-series for real characters in 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 representations; Mordell-Weil lattices; elliptic curves; deformation theory of isolated singularities; Mordell-Weil group; Hasse zeta function; elliptic surfaces; Artin L-function; Weil height; del Pezzo surfaces; cubic forms Shioda, T.: Mordell-Weil lattices and Galois representation. I, II, III. Proc. Japan Acad., 65A, 269-271 ; 296-299 ; 300-303 (1989). Arithmetic varieties and schemes; Arakelov theory; heights, Galois theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic surfaces, elliptic or Calabi-Yau fibrations, General ternary and quaternary quadratic forms; forms of more than two variables, Elliptic curves over global fields, Elliptic curves Mordell-Weil lattices and Galois representation. III
| 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 fields; tame fundamental group; Markoff triples; tamely ramified covers; characteristic \(p\); covers of curves Curves over finite and local fields, Coverings of curves, fundamental group Tamely ramified covers of the projective line with alternating and symmetric 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 \(x^n+y^m+1=0\) algebraic number fields; algebraic function fields; algebraic \(p\)-adic height pairing; elliptic curve; Selmer group; complex multiplication; pairing of Galois cohomology groups; Poincaré group; Galois extension Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On a Galois extension with restricted ramification related to the Selmer group of an elliptic curve with complex multiplication
| 0 |
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 \(x^n+y^m+1=0\) Artin-Schreier extensions of function fields; automorphisms; \(k\)-error linear complexity; joint linear complexity; multisequences Cryptography, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Shift register sequences and sequences over finite alphabets in information and communication theory Multisequences with large linear and \(k\)-error linear complexity from a tower of Artin-Schreier extensions of function fields
| 0 |
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 Cremona group; automorphism of the affine space; tame automorphisms Group actions on affine varieties, Birational automorphisms, Cremona group and generalizations An arbitrary nonlinear automorphism of the affine space \(A^3\) with the affine group generate the group of the tame automorphisms \(A^3\)
| 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 \(x^n+y^m+1=0\) explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press \(\zeta (s)\) and \(L(s, \chi)\), Research exposition (monographs, survey articles) pertaining to number theory, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Distribution of primes An introduction to the theory of the Riemann zeta-function.
| 0 |
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 curves over global fields; arithmetic function fields; sheaves of differentials; Kähler differentials; arithmetic schemes; valuation rings Kunz, E.; Waldi, R.: Integral differentials of elliptic function fields. Abh. math. Sem. univ. Hamburg 74, 243-252 (2004) Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry, Valuation rings Integral differentials of elliptic function fields
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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 \(x^n+y^m+1=0\) linear algebraic groups; pseudo-reductive groups; generalized standard construction; groups locally of minimal type; structure and classification of pseudo-reductive groups; imperfect fields; pseudo-split groups; central extensions; affine group schemes Conrad, B.; Prasad, G., Classification of pseudo-reductive groups, Annals of Mathematics Studies, (2015), Princeton University Press Linear algebraic groups over arbitrary fields, Structure theory for linear algebraic groups, Affine algebraic groups, hyperalgebra constructions, Linear algebraic groups over local fields and their integers Classification of pseudo-reductive groups.
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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 \(x^n+y^m+1=0\) Mordell-Weil theorem; rational points; \(p\)-descent; Selmer group; \(L\)- function; conjecture of Birch and Swinnerton-Dyer; Igusa curves Ulmer, D. L., P-descent in characteristic p, Duke Math. J., 62, 2, 237-265, (1991) Elliptic curves, Rational points, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves \(p\)-descent in characteristic \(p\)
| 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 function fields; algebraic curves; Riemann-Roch theorem; coding theory; algebraic-geometry codes; differentials; towers of functions fields; Tsfasman-Vladut-Zink theorem; trace codes Stichtenoth, H., \textit{Algebraic Function Fields and Codes}, 254, (2009), Springer, Berlin Algebraic functions and function fields in algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects) Algebraic function fields and codes
| 0 |
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 defined over a valuation ring; function field; first order language of valued fields; stable reduction theorem [GMP] B. W. Green, M. Matignon and F. Pop,On valued function fields III, Reductions of algebraic curves, Journal für die Reine und Angewandte Mathematik432 (1992), 117--133. Arithmetic ground fields for curves, Valued fields, First-order arithmetic and fragments On valued function fields. III: Reductions of algebraic curves. Appendix (by Ernst Kani): The stable reduction theorem via moduli theory
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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 \(x^n+y^m+1=0\) moduli space of smooth affine curves; curves with one place at infinity; genus; quotient space; automorphism group; rational variety Oka, M.: Moduli space of smooth affine curves of a given genus with one place at infinity. Prog. math. 162, 409-434 (1998) Families, moduli of curves (algebraic), Special algebraic curves and curves of low genus Moduli space of smooth affine curves of a given genus with one place at infinity
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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 \(x^n+y^m+1=0\) group of automorphisms; birational splitting theorem for the Albanese map; Albanese variety; meromorphic function field Rational and birational maps, Automorphisms of curves, Birational automorphisms, Cremona group and generalizations, Automorphisms of surfaces and higher-dimensional varieties Meromorphic function fields of Albanese 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 \(x^n+y^m+1=0\) linear algebraic group; R-equivalence; function fields of surfaces; weak approximation; Hasse principle Colliot-Thélène, J.-L.; Gille, P.; Parimala, R., Arithmetic of linear algebraic groups over two-dimensional geometric fields, Duke Math. J., 121, 285-341, (2004) Forms of degree higher than two, Modular and Shimura varieties, Linear algebraic groups over adèles and other rings and schemes, Linear algebraic groups over arbitrary fields, Global ground fields in algebraic geometry Arithmetic of linear algebraic groups over 2-dimensional geometric fields
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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 \(x^n+y^m+1=0\) curves of genus greater than one; computational aspects; number of points; Jacobian; finite fields; Mordell-Weil group; construction of curves Poonen, Bjorn, Computational aspects of curves of genus at least \(2\). Algorithmic number theory, Talence, 1996, Lecture Notes in Comput. Sci. 1122, 283-306, (1996), Springer, Berlin Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic curves Computational aspects of curves of genus at least 2
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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 \(x^n+y^m+1=0\) valued function fields; existence of regular functions; Henselian constant field; divisor reduction map; divisor group; elementary class Green, B.; Matignon, M.; Pop, F.: On valued function fields II: Regular functions and elements with the uniqueness property. J. reine angew. Math. 412, 128-149 (1990) Valued fields, Algebraic functions and function fields in algebraic geometry, Model theory of fields, Arithmetic theory of algebraic function fields, Field extensions On valued function fields. II: Regular functions and elements with the uniqueness property
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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 \(x^n+y^m+1=0\) Brauer group of function field; reciprocity sequence; higher-dimensional function fields; smooth projective varieties; threefolds J. -L. Colliot-Thélène, ''On the reciprocity sequence in the higher class field theory of function fields,'' in Algebraic \(K\)-Theory and Algebraic Topology, Dordrecht: Kluwer Acad. Publ., 1993, vol. 407, pp. 35-55. Generalized class field theory (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic theory of algebraic function fields, Geometric class field theory, Étale and other Grothendieck topologies and (co)homologies On the reciprocity sequence in the higher class field theory of function fields
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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 \(x^n+y^m+1=0\) affine variety minus bound on the height of integral points; hyperplanes in general position; number of integral points; function fields Wang, J.T.-Y., \textit{S}-integral points of \(\mathbb{P}^n - \{2 n + 1 \text{ hyperplanes in general position} \}\) over number fields and function fields, Trans. amer. math. soc., 348, 3379-3389, (1996) Arithmetic theory of algebraic function fields, Rational points, Varieties over global fields \(S\)-integral points of \(\mathbb{P}^ n- \{2n+1\) hyperplanes in general position\(\}\) over number fields and function fields
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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 \(x^n+y^m+1=0\) classification of real affine cubic curves; action of the group of affine isomorphisms Weinberg D.A: affine classification of cubic curves. Rocky Mt. J. Math. 18(3), 655--664 (1988) Special algebraic curves and curves of low genus, Projective techniques in algebraic geometry, Questions of classical algebraic geometry, Group actions on varieties or schemes (quotients) The affine classification of cubic curves
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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 \(x^n+y^m+1=0\) curves in characteristic p; p-adic Galois representations; group of automorphisms; Jacobian variety; Tate module R. Valentini,Some p-adic Galois representations for curves in characteristic p, Mathematische Zeitschrift192 (1986), 541--545. Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Iwasawa theory, Galois theory Some \(p\)-adic Galois representations for curves in characteristic \(p\)
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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 \(x^n+y^m+1=0\) moduli space of curves; mapping class group; Riemann zeta function; Euler characteristic; configurations HZ J.~Harer and D.~Zagier, \emph The Euler characteristic of the moduli space of curves, Invent. Math. \textbf 85 (1986), no.~3, 457--485. Topological properties in algebraic geometry, \(\zeta (s)\) and \(L(s, \chi)\), Families, moduli of curves (algebraic) The Euler characteristic of the moduli space of curves
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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 \(x^n+y^m+1=0\) elliptic curves over finite fields; Weil conjectures; group of torsion; elliptic curves over local fields; good reduction; elliptic curves over global fields; Mordell-Weil theorem; descent; Selmer group; Shafarevich groups J. H. Silverman, \textit{The Arithmetic of Elliptic Curves.}Springer Verlag, New York, 1986. Elliptic curves over global fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Elliptic curves over local fields, Curves over finite and local fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Special algebraic curves and curves of low genus, Rational points, Arithmetic ground fields for curves, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Elliptic curves, Cubic and quartic Diophantine equations The arithmetic of elliptic curves
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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 \(x^n+y^m+1=0\) algebraic geometry; Riemann hypothesis; function fields; Severi's algebraic theory of correspondences on algebraic curves André Weil [3] On the Riemann hypothesis in function-fields , Proceedings of the National Academy of Sciences, vol. 27 (1941), pp. 345-347. Duke University. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields On the Riemann hypothesis in function-fields
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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 \(x^n+y^m+1=0\) curves of genus two; Jacobians; local fields; number fields; canonical height; height constant; Mordell-Weil group Stoll M., On the height constant for curves of genus two. II, Acta Arith. 104 (2002), 165-182. Heights, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry On the height constant for curves of genus two. II
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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 \(x^n+y^m+1=0\) automorphisms of curves; Nottingham group; cohomology of groups; Harbater-Katz-Gabber curves; algebraic covers Coverings of curves, fundamental group, Limits, profinite groups, Cohomology of groups A cohomological treatise of HKG-covers with applications to the Nottingham group
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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 \(x^n+y^m+1=0\) characteristic \(p\); formal schemes; Galois cover of algebraic curve; Abhyankar's conjecture; fundamental group of affine curves David Harbater, ``Abhyankar's conjecture on Galois groups over curves'', Invent. Math.117 (1994) no. 1, p. 1-25 Coverings of curves, fundamental group, Representations of groups as automorphism groups of algebraic systems, Coverings in algebraic geometry Abhyankar's conjecture on Galois groups over curves
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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 \(x^n+y^m+1=0\) \(\dagger\)-adic algebras; \(p\)-adic de Rham cohomology; \(p\)-adic de Rham complex; factorization of the zeta function; functoriality; group of automorphisms; transfer module; special module; \(p\)-adic differential operators; cohomological operations; flat liftings; \(\dagger\)-adic schemes; infinitesimal site; Gysin sequence; infinitesimal topos Arabia, A.; Mebkhout, Z., Sur le topos infinitésimal \textit{p}-adique d\(###\)un schéma lisse I, Ann. Inst. Fourier, 60, 6, 1905-2094, (2010) \(p\)-adic cohomology, crystalline cohomology, \(p\)-adic differential equations, Commutative rings of differential operators and their modules, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, de Rham cohomology and algebraic geometry, Finite ground fields in algebraic geometry Infinitésimal \(p\)-adic topos of a smooth scheme. I.
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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 \(x^n+y^m+1=0\) affine space; polynomials over commutative rings; group of polynomial automorphisms; group of tame automorphisms Berson, Joost: The tame automorphism group in two variables over basic Artinian rings, J. algebra 324, 530-540 (2010) Polynomials over commutative rings, Actions of groups on commutative rings; invariant theory, Birational automorphisms, Cremona group and generalizations, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) The tame automorphism group in two variables over basic Artinian rings
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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 \(x^n+y^m+1=0\) arithmetic of elliptic curves; determining the group of rational points; Mordell-Weil theorem; Birch and Swinnerton-Dyer conjecture; Hasse-Weil L-series; effective determination of all imaginary quadratic fields with given class number; Iwasawa theory; main conjecture for elliptic curves; descent method Coates, J.: Elliptic curves and Iwasawa theory. In: Modular forms. Rankin, R.A. (ed.), pp. 51-73. Chichester: Ellis Horwood Ltd (1984) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Research exposition (monographs, survey articles) pertaining to number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Elliptic curves and Iwasawa theory
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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 \(x^n+y^m+1=0\) elliptic curves; complex multiplication; abelian varieties; zeta function; modular functions; theta functions; periods of integrals; class fields; field of moduli of a polarized abelian variety; Hecke \(L\)-functions; periods of abelian integrals; period symbol; differential forms; polarizations Shimura, G., \textit{abelian varieties with complex multiplication and modular functions}, (1998), Princeton University Press, Princeton, NJ Discontinuous groups and automorphic forms, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic moduli of abelian varieties, classification, Analytic theory of abelian varieties; abelian integrals and differentials, Complex multiplication and abelian varieties, Theta functions and abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Abelian varieties with complex multiplication and modular functions
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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 \(x^n+y^m+1=0\) function fields; class group; continued fractions; generalization of Hirzebruch's theorem; class number González, CD, Class numbers of quadratic function fields and continued fractions, J. Number Theory, 40, 38-59, (1992) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Continued fractions, Jacobians, Prym varieties, Finite ground fields in algebraic geometry Class numbers of quadratic function fields and continued fractions
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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 \(x^n+y^m+1=0\) automorphisms group of Macbeath curve; algebraic curves associated with subgroups of finite index in the; modular group; non-congruence subgroups; covering of the projective line; Hurwitz group; algebraic curves associated with subgroups of finite index in the modular group Klaus Wohlfahrt, Macbeath's Curve and the Modular Group, Glasg. Math. J.27 (1985), p. 239-247 - ISSN : 2118-8572 (online) 1246-7405 (print) - Société Arithmétique de Bordeaux Coverings of curves, fundamental group, Arithmetic ground fields for curves, Structure of modular groups and generalizations; arithmetic groups, Special algebraic curves and curves of low genus, Singularities of curves, local rings, Unimodular groups, congruence subgroups (group-theoretic aspects), Subgroup theorems; subgroup growth, Finite automorphism groups of algebraic, geometric, or combinatorial structures Macbeath's curve and the modular group
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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 \(x^n+y^m+1=0\) error-correcting code; \(C_{ab}\) curves; towers of algebraic function fields; genus Shor, Caleb McKinley, Genus calculations for towers of functions fields arising from equations of \(C_{ab}\) curves, Albanian J. Math., 5, 1, 31-40, (2011) Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry Genus calculations for towers of function fields arising from equations of \(C_{ab}\) curves
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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 \(x^n+y^m+1=0\) characterization of the complex affine plane; simply connected algebraic curves; Ramanujam surfaces; hyperbolic complex analysis; regular actions of the group \({\mathbb{C}}^*\) Zaidenberg M G, Isotrivial families of curves on affine surfaces and characterizations of the affine plane,Math. USSR. Izvestiya,30 (1988) 503--532 Rational and ruled surfaces, Structure of families (Picard-Lefschetz, monodromy, etc.), Hyperbolic and Kobayashi hyperbolic manifolds, Special surfaces, Families, moduli of curves (algebraic) Isotrivial families of curves on affine surfaces and characterization of the affine plane
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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 \(x^n+y^m+1=0\) spacing distributions of zeros; zeros of the Riemann zeta-function; zeta functions of curves over finite fields; Montgomery-Odlyzko law; Ramanujan \(L\)-function; pair correlation; random matrix models; symplectic symmetry Katz, N.M., Sarnak, P.: Zeroes of zeta functions and symmetry. Bull. Am. Math. Soc. (N.S.) \textbf{36}(1), 1-26 (1999b) \(\zeta (s)\) and \(L(s, \chi)\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Other Dirichlet series and zeta functions, General mathematical topics and methods in quantum theory Zeroes of zeta functions and symmetry
| 0 |
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 curves over function fields; Mordell-Weil lattices; \(L\)-function of an elliptic curve over a function field T. Shioda, Some remarks on elliptic curves over function fields , Astérisque 209 (1992), 12, 99-114. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Rational points, Elliptic curves over global fields, Algebraic functions and function fields in algebraic geometry Some remarks on elliptic curves over function fields
| 0 |
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 curve over a finite field; group of automorphisms; rational group ring; zeta-functions of the quotient curves DOI: 10.4153/CMB-1990-046-x Coverings of curves, fundamental group, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Group actions on varieties or schemes (quotients) A note on relations between the zeta-functions of Galois coverings of 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 \(x^n+y^m+1=0\) finite fields; character sums; Weil conjectures; Riemann-Roch theorem; points on curves over finite fields; zeta-functions; \(L\)-functions; idele class characters; modular forms; automorphic representations; Ramanujan graphs; Alon-Boppana theorem; regular graphs; Riemann hypothesis for zeta functions of curves over finite fields; exponential sums; Cayley graphs; finite upper half plane graphs; valuations of function fields; projective curve; Hecke operators; automorphic representations of quaternion groups; expander; simple random walk; spectral theory of graphs Li, W. -C. Winnie: Number theory with applications. Series of university mathematics 7 (1996) Research exposition (monographs, survey articles) pertaining to number theory, Modular and automorphic functions, Graph theory, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Representation-theoretic methods; automorphic representations over local and global fields, Holomorphic modular forms of integral weight, Estimates on exponential sums, Exponential sums, Adèle rings and groups, Representations of Lie and linear algebraic groups over global fields and adèle rings, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Number theory with applications
| 0 |
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 \(x^n+y^m+1=0\) dilogarithm; \(K\)-theory of fields; hyperbolic geometry; Dedekind function; polylogarithms; motivic complexes; Zagier's conjecture; curves; regulators; special values of \(L\)-functions; motivic Lie algebra; framed mixed Tate motives; hyperlogarithms A. Goncharov, \textit{Polylogarithms in arithmetic and geometry}, \textit{Proc. ICM}\textbf{1-2} (1995) 374. Zeta functions and \(L\)-functions of number fields, \(K\)-theory of global fields, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Polylogarithms in arithmetic and geometry
| 0 |
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 biregular automorphisms; complex K3 surfaces; nodal curves on a K3-like surface; anticanonical basic surface B. Harbourne, ``Automorphisms of K\(3\)-like rational surfaces'' in Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) , Proc. Symp. Pure Math. 46 , Part 2, Amer. Math. Soc., Providence, 1987, 17-28. Special surfaces, Group actions on varieties or schemes (quotients), Rational and unirational varieties, \(K3\) surfaces and Enriques surfaces, Picard groups Automorphisms of K3-like rational 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 \(x^n+y^m+1=0\) rationality of function fields; field of invariants; action of finite group; non ramified Brauer group; rationality problems; Noether problem D. J. Saltman, ''Multiplicative field invariants,''J. Algebra,106, 221--238 (1987). Brauer groups of schemes, Arithmetic theory of algebraic function fields, Rational and unirational varieties, Galois cohomology, Transcendental field extensions, Group actions on varieties or schemes (quotients), Geometric invariant theory, Separable extensions, Galois theory Multiplicative 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 \(x^n+y^m+1=0\) point-line arrangements; orchard problem; elliptic curves; group law; application of finite fields Planar arrangements of lines and pseudolines (aspects of discrete geometry), Elliptic curves, Computational aspects of algebraic curves Orchards in elliptic 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 \(x^n+y^m+1=0\) singular curves over finite fields; rationality of the zeta function; functional equation of the zeta function; singular Riemann-Roch theorem Galindo, W. Zúñiga: Zeta functions of singular algebraic curves over finite fields. (1996) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves, Curves over finite and local fields, Jacobians, Prym varieties, \(\zeta (s)\) and \(L(s, \chi)\), Riemann-Roch theorems Zeta functions of singular 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 \(x^n+y^m+1=0\) hyperelliptic curves; automorphisms; marked points; moduli space; Euler characteristic; symmetric group; generating function Gorsky, E.: On the sn-equivariant Euler characteristic of moduli spaces of hyperelliptic curves, Math. res. Lett. 16, No. 4, 591-603 (2009) Moduli, classification: analytic theory; relations with modular forms, Families, moduli of curves (algebraic), Finite automorphism groups of algebraic, geometric, or combinatorial structures On the \(S_n\)-equivariant Euler characteristic of moduli spaces of 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 \(x^n+y^m+1=0\) recursive towers of function fields over finite fields; elliptic modular curves Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Modular and Shimura varieties, Compact Riemann surfaces and uniformization, Families, moduli of curves (analytic) Towers of function fields over finite fields corresponding to elliptic 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 \(x^n+y^m+1=0\) second generalized Giulietti-Korchmáros function fields; maximal function fields; genus spectrum of maximal curves Curves over finite and local fields, Arithmetic ground fields for curves, Automorphisms of curves On subfields of the second generalization of the GK maximal function 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 \(x^n+y^m+1=0\) linear groups; real curves; projective curves; function fields; strong Hasse principle; homogeneous spaces; existence of \(K\)-rational points; weak approximation; density of local points; diagonal image; central isogeny; principal homogeneous spaces; projective algebraic varieties; reciprocity law; obstruction to the Hasse principle; obstruction to weak approximation; Galois cohomology Jean-Louis Colliot-Thélène, Groupes linéaires sur les corps de fonctions de courbes réelles, J. Reine Angew. Math. 474 (1996), 139 -- 167 (French). Galois cohomology of linear algebraic groups, Algebraic functions and function fields in algebraic geometry, Real algebraic and real-analytic geometry, Linear algebraic groups over adèles and other rings and schemes, Homogeneous spaces and generalizations Linear groups on the function fields of real 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 curves; algebraic function fields; automorphism groups of curves in positive characteristic; Stöhr-Voloch theory; curves with many points over finite fields Hirschfeld, J. W.P.; Korchmáros, G.; Torres, F., Algebraic Curves over a Finite Field, Princeton Series in Applied Mathematics, (2008), Princeton University Press: Princeton University Press Princeton, NJ, MR 2386879 Curves over finite and local fields, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Finite ground fields in algebraic geometry, Positive characteristic ground fields in algebraic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Divisors, linear systems, invertible sheaves, Arithmetic ground fields for curves Algebraic curves over a finite 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 \(x^n+y^m+1=0\) Galois group; inverse Galois theory; Mathieu groups; finite simple groups; embedding problems; rigidity method; Hilbertian fields; function fields; absolute Galois group; generating polynomials of Galois groups Research exposition (monographs, survey articles) pertaining to field theory, Inverse Galois theory, Separable extensions, Galois theory, Galois cohomology, Rigid analytic geometry Inverse Galois 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 \(x^n+y^m+1=0\) constructive Galois theory; fundamental group; field of definition; ramification structures; topological automorphisms; algebraic; function field; \(PSL_ 2({\mathbb{F}}_ p)\) Matzat, B.H.: Topologische Automorphismen in der konstruktiven Galoistheorie. Erscheint demnächst Galois theory, Arithmetic theory of algebraic function fields, Representations of groups as automorphism groups of algebraic systems, Compact Riemann surfaces and uniformization, Infinite automorphism groups, Simple groups: alternating groups and groups of Lie type, Coverings of curves, fundamental group Topologische Automorphismen in der konstruktiven Galoistheorie. (Topological automorphisms in constructive Galois 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 \(x^n+y^m+1=0\) Galois theory of algebraic numbers; hypermaps; Riemann surface; Belyi function; dessins d'enfants; Galois group; congruence subgroups; modular group; elliptic curves Jones, G. A.; Singerman, D., Belyǐ functions, hypermaps and Galois groups, Bull. Lond. Math. Soc., 28, 561-590, (1996) Riemann surfaces; Weierstrass points; gap sequences, Galois theory, Planar graphs; geometric and topological aspects of graph theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Coverings of curves, fundamental group, Structure of modular groups and generalizations; arithmetic groups, Geometric group theory, Compact Riemann surfaces and uniformization Belyĭ functions, hypermaps and Galois 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 \(x^n+y^m+1=0\) global function fields; rational places; curves over finite fields; asymptotic measure of \(\mathbb{F}_q\)-rational points; class field towers; codes; Gilbert-Varshamov bound Niederreiter, H.; Xing, C., Towers of global function fields with asymptotically many rational places and an improvement on the Gilbert-varshamov bound, Math. Nachr., 195, 171-186, (1998) Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Bounds on codes Towers of global function fields with asymptotically many rational places and an improvement on the Gilbert-Varshamov bound
| 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 \(x^n+y^m+1=0\) geometric Goppa codes; generalized algebraic geometry codes; code automorphisms; automorphism groups of function fields; algebraic function fields Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Automorphisms of curves, Algebraic functions and function fields in algebraic geometry On the automorphisms of generalized 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 \(x^n+y^m+1=0\) loop groups; affine Lie algebras; moduli of \(G\) bundles on curves; embeddings of reductive groups; representation theory; spherical varieties; wonderful compactification; torus group; Harish-Chandra transform; character sheaves; ind-scheme; compactification; flag varieties; divisors in ind-schemes Solis, P., A wonderful embedding of the loop group Compactifications; symmetric and spherical varieties, Representations of Lie and linear algebraic groups over real fields: analytic methods A wonderful embedding of the loop 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 \(x^n+y^m+1=0\) Brauer groups; curves over local fields; \(p\)-adic curves; field extensions; resolutions of singularities; algebraic function fields; curves over rings of integers of \(p\)-adic fields Saltman, D. J., Division algebras over \(p\)-adic curves, J. Ramanujan Math. Soc., 12, 25-47, (1997) Finite-dimensional division rings, Curves over finite and local fields, Arithmetic ground fields for curves, Brauer groups of schemes, Skew fields, division rings, Algebras and orders, and their zeta functions, Singularities of curves, local rings, Algebraic functions and function fields in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Local ground fields in algebraic geometry Division algebras over \(p\)-adic 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 \(x^n+y^m+1=0\) sums of squares; real affine algebraic curves; real hyperelliptic curves; Picard group J. Huisman, L. Mahé, Geometrical aspects of the level of curves, J. Alg., Preprint, 2001. Algebraic functions and function fields in algebraic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Jacobians, Prym varieties, Real algebraic and real-analytic geometry Geometrical aspects of the level 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 \(x^n+y^m+1=0\) period map; Schottky groups parametrized by a rigid analytic space; family of Mumford curves; p-adic Siegel half space; de Rham cohomology group; infinite automorphic product; Gauss-Manin connection; Tate curve; principal theta function L. Gerritzen,Periods and Gauss-Manin connection for families of p-adic Schottky groups, Math. Ann.275 (1986), 425--453. Local ground fields in algebraic geometry, Families, moduli of curves (analytic), Period matrices, variation of Hodge structure; degenerations, de Rham cohomology and algebraic geometry Periods and Gauss-Manin connection for families of p-adic Schottky 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 \(x^n+y^m+1=0\) arithmetic over function fields; arithmetic of algebraic curves; Mordell Weil theorem; Mordell conjecture Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Heights, Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Diophantine geometry on curves 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 \(x^n+y^m+1=0\) function field of one variable; fundamental group of the affine curve; absolute Galois group Coverings of curves, fundamental group, Galois theory, Homotopy theory and fundamental groups in algebraic geometry, Algebraic functions and function fields in algebraic geometry The projectivity of the fundamental group of an affine line
| 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 \(x^n+y^m+1=0\) Brauer groups; curves over local fields; field extensions; resolutions of singularities; algebraic function fields; curves over rings of integers of \(p\)-adic fields D. J. Saltman, ''Correction to: ``Division algebras over \(p\)-adic curves'' [J. Ramanujan Math. Soc. 12 (1997), no. 1, 25-47; MR1462850 (98d:16032)],'' J. Ramanujan Math. Soc., vol. 13, iss. 2, pp. 125-129, 1998. Finite-dimensional division rings, Curves over finite and local fields, Arithmetic ground fields for curves Correction to: Division algebras over \(p\)-adic 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 \(x^n+y^m+1=0\) abelian fields of small degree; coverings of modular curves; unit group; one-parameter families of elliptic curves O. Lecacheux, Units in number fields and elliptic curves, in: Advances in Number Theory (Kingston, ON, 1991), Oxford Univ. Press, New York, 1993, 293--301. Units and factorization, Elliptic curves Units in number fields and 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 \(x^n+y^m+1=0\) homology of algebraic curves; automorphisms; mapping class group; absolute Galois group; combinatorial group theory Group actions on varieties or schemes (quotients), Automorphisms of curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Braid groups; Artin groups Group actions on cyclic covers of the projective line
| 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; lifting of automorphisms of curves; \(p\)-adic discs; curves over local fields; characteristic \(p\); Witt vectors; Kummer-Artin-Schreier-Witt theory B. Green and M. Matignon, ''Liftings of Galois covers of smooth curves,'' Compositio Math., vol. 113, iss. 3, pp. 237-272, 1998. Automorphisms of curves, Local ground fields in algebraic geometry, Curves over finite and local fields, Coverings of curves, fundamental group Liftings of Galois covers of smooth 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 \(x^n+y^m+1=0\) elliptic curves over function fields; explicit computation of \(L\)-functions; BSD conjecture; unbounded ranks; explicit Jacobi sums Varieties over finite and local fields, Zeta and \(L\)-functions in characteristic \(p\), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Gauss and Kloosterman sums; generalizations A new family of elliptic curves with unbounded rank
| 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 \(x^n+y^m+1=0\) characterization of finite group of polynomial automorphisms; algebraic compactification Furushima, M.: Finite groups of polynomial automorphisms in ? n . Tohoku Math. J.35, 415-424 (1983) Complex Lie groups, group actions on complex spaces, Group actions on varieties or schemes (quotients) Finite groups of polynomials automorphisms in \({\mathbb{C}}^ n\)
| 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 \(x^n+y^m+1=0\) elliptic curves; cryptosystems; discrete logarithm; group of rational points; elliptic curve over a finite field; practical implementations; algorithms; running times R. Harasawa, J. Shikata, J. Suzuki, H. Imai, Comparing the MOV and FR reductions in elliptic curve cryptography, in: Advances in Cryptology--Eurocrypt '99, Lecture Notes in Computer Science, Vol. 1592, Springer, Berlin, 1999, pp. 190--205. Cryptography, Applications to coding theory and cryptography of arithmetic geometry Comparing the MOV and FR reductions in elliptic curve cryptography
| 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 \(x^n+y^m+1=0\) forms over number fields; Hasse principle; affine variety; Hardy-Littlewood circle method; asymptotic formula; number of solutions; weak approximation C.\ M. Skinner, Forms over number fields and weak approximation, Compos. Math. 106 (1997), 11-29. Forms of degree higher than two, Applications of the Hardy-Littlewood method, Diophantine equations in many variables, Global ground fields in algebraic geometry, Varieties over global fields Forms over number fields and weak approximation
| 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 of positive characteristic; arithmetic fundamental group; Galois representation; automorphic representation G. Böckle and C. Khare, Finiteness results for mod \(l\) Galois representations over function fields, Galois representations, Representation-theoretic methods; automorphic representations over local and global fields, Coverings of curves, fundamental group, Galois cohomology Mod \(\ell\) representations of arithmetic fundamental groups. I: An analog of Serre's conjecture for function fields
| 0 |
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 \(x^n+y^m+1=0\) inverse Galois problem; canonical form; linear automorphisms; monomial automorphisms; fields of rational functions; survey Hajja, M.: Linear and monomial automorphisms of fields of rational functions: some elementary issues, Algebra and number theory (2000) Inverse Galois theory, Research exposition (monographs, survey articles) pertaining to field theory, Transcendental field extensions, Actions of groups on commutative rings; invariant theory, Rationality questions in algebraic geometry Linear and monomial automorphisms of fields of rational functions: Some elementary issues
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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 \(x^n+y^m+1=0\) \(p\)-adic \(L\)-functions; elliptic curves; rational points; cyclotomic characters; interpolation; projective limit of the group of global units; \(p\)-adic height Perrin-Riou, Bernadette, Fonctions \(L\) \(p\)-adiques d'une courbe elliptique et points rationnels, Ann. Inst. Fourier (Grenoble), 0373-0956, 43, 4, 945-995, (1993) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Zeta functions and \(L\)-functions of number fields, Galois cohomology, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) \(p\)-adic \(L\)-functions of an elliptic curve and 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 \(x^n+y^m+1=0\) Brauer group of rational function field over complex field Brauer groups of schemes, Galois cohomology Groupe de Brauer et topologie des variétés algébriques complexes lisses. (Brauer group and topology of smooth complex algebraic varieties)
| 0 |
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 \(x^n+y^m+1=0\) hyperbolic curve; group of biholomorphic automorphisms; fundamental group Shabat, GB, Local reconstruction of complex algebraic surfaces from universal coverings, Funktsional. Anal. i Prilozhen., 17, 90-91, (1983) Coverings in algebraic geometry, Special surfaces, Complex Lie groups, group actions on complex spaces, Transcendental methods of algebraic geometry (complex-analytic aspects), Low codimension problems in algebraic geometry, Group actions on varieties or schemes (quotients), Homotopy theory and fundamental groups in algebraic geometry Local construction of complex algebraic surfaces with respect to the universal covering
| 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 \(x^n+y^m+1=0\) diagonal equations; cyclotomic classes; cyclotomic numbers; number of points on finite diagonal curves; finite fields Curves over finite and local fields, Cyclotomy, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Counting the number of points on affine diagonal curves
| 0 |
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 \(x^n+y^m+1=0\) abelian Galois extensions; relative Brauer groups; cyclic extensions; indecomposable division algebras of prime exponent; central simple algebras; Brauer class; rational function fields Finite-dimensional division rings, Equations in general fields, Valued fields, Brauer groups of schemes, Separable extensions, Galois theory Dec groups for arbitrarily high exponents
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