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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; Galois covering of complete curve; p-group operating on curves Coverings of curves, fundamental group, Arithmetic ground fields for curves Sur la formule de Deuring-Šafarevič et un résultat de Nakajima. (On the Deuring-Shafarevich formula and a result by Nakajima)
| 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 \(x^n+y^m+1=0\) Severi-Brauer surface; group of birational automorphisms Birational automorphisms, Cremona group and generalizations, Automorphisms of surfaces and higher-dimensional varieties Birational automorphisms of Severi-Brauer 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 \(x^n+y^m+1=0\) Mumford curves; stable curves; action of a free group; tree of projective lines; formal Teichmüller space Coverings of curves, fundamental group, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Local ground fields in algebraic geometry The formal Teichmüller space for stable Mumford 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 \(x^n+y^m+1=0\) Birch-Swinnerton-Dyer conjecture; sums of squares; class number problem; imaginary quadratic fields; Gauss' conjecture; modular elliptic curve; Hasse-Weil L-function; class-number-one problem \BibAuthorsD. Goldfeld, Gauss' class number problem for imaginary quadratic fields, Bull. Amer. Math. Soc. 13 (1) (1985), 23--37. Class numbers, class groups, discriminants, Quadratic extensions, Algebraic number theory computations, Elliptic curves over global fields, History of mathematics in the 18th century, History of number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Holomorphic modular forms of integral weight Gauss' class number problem for imaginary quadratic fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of curves; algebraic group actions; Hilbert's fourteenth problem; stability; toric varieties Dolgachev, I. V., Introduction to geometric invariant theory, Lecture Notes Series, vol. 25, (1994), Seoul National University, Research Institute of Mathematics, Global Analysis Research Center Seoul Geometric invariant theory, Group actions on varieties or schemes (quotients), Toric varieties, Newton polyhedra, Okounkov bodies, Research exposition (monographs, survey articles) pertaining to algebraic geometry Introduction to geometric invariant 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 \(x^n+y^m+1=0\) mean values of \(L\)-functions; finite fields; function fields 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) The moments and statistical distribution of class number of primes 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 \(x^n+y^m+1=0\) irreducible closed semialgebraic set; orders of function fields; real algebraic sets Andradas, C.; Gamboa, J. M., On projections of real algebraic varieties, Pacific J. Math., 121, 2, 281-291, (1986) Real algebraic and real-analytic geometry, Real-analytic and Nash manifolds, Ordered fields On projections of real 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 \(x^n+y^m+1=0\) tower of function fields; number of rational places; ihara's constant; cartier operator; \(p\)-rank N. Anbar, P. Beelen, N. Nguyen, A new tower meeting Zink's bound with good \(p\)-rank, appeared online 18 January 2017 in Acta Arithmetica. Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry A new tower with good \(p\)-rank meeting Zink's 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 \(x^n+y^m+1=0\) Igusa compactification; Siegel modular variety; moduli space of genus 2 curves; Weierstrass points; zeta function; characteristic p; Weil conjectures Ronnie Lee and Steven H. Weintraub, Cohomology of a Siegel modular variety of degree 2, Group actions on manifolds (Boulder, Colo., 1983) Contemp. Math., vol. 36, Amer. Math. Soc., Providence, RI, 1985, pp. 433 -- 488. Families, moduli, classification: algebraic theory, Theta series; Weil representation; theta correspondences, Classical real and complex (co)homology in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties, Automorphic functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Cohomology of a Siegel modular variety of degree 2
| 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 \(x^n+y^m+1=0\) differential Galois theory of infinite dimension; differential fields; Lie-Ritt functor; algebraic group scheme Umemura H., Differential Galois theory of infinite dimension, Nagoya Math. J.144 (1996) 59-135. Zbl0878.12002 MR1425592 Differential algebra, Group actions on varieties or schemes (quotients) Differential Galois theory of infinite dimension
| 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 \(\mu\)-invariant; elliptic curves over global fields; Greenberg's conjecture; Selmer group Mak Trifković, On the vanishing of \(\mu \)-invariants of elliptic curves over \(\mathbb Q\), Canad. J. Math. 57 (2005), no. 4, 812-843. Iwasawa theory, Elliptic curves over global fields, Elliptic curves On the vanishing of \(\mu\)-invariants of elliptic curves over \(\mathbb Q\)
| 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 action of a finite group on complex affine space; fixed point Model-theoretic algebra, Group actions on varieties or schemes (quotients), Fixed points and coincidences in algebraic topology Algebraic actions of \(p\)-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 \(x^n+y^m+1=0\) modular function; normalized generator of a function field; moonshine; complex multiplication; class fields over imaginary quadratic fields Chang Heon Kim and Ja Kyung Koo, Arithmetic of the modular function \?_{1,4}, Acta Arith. 84 (1998), no. 2, 129 -- 143. Modular and automorphic functions, Relationship to Lie algebras and finite simple groups, Holomorphic modular forms of integral weight, Algebraic numbers; rings of algebraic integers, Class field theory, Special algebraic curves and curves of low genus Arithmetic of the modular function \(j_{1,4}\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) plane quartic curves; function field; Galois group K. Miura - H. Yoshihara, Field theory for function fields of plane quartic curves, J. Algebra, 226 (2000), pp. 283-294. Zbl0983.11067 MR1749889 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Field theory for function fields of plane quartic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) representation theory; reductive algebraic groups; simple modules; highest weights; character formulas; Weyl's character formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology rings; rings of regular functions; Schubert schemes; line bundles; Schur algebras; quantum groups; Kazhdan-Lusztig polynomials J. C. Jantzen, \textit{Representations of Algebraic Groups. Second edition}, Amer. Math. Soc., Providence (2003). Representation theory for linear algebraic groups, Cohomology theory for linear algebraic groups, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory, Group schemes, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Affine algebraic groups, hyperalgebra constructions, Linear algebraic groups over arbitrary fields Representations of algebraic 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 \(x^n+y^m+1=0\) transcendental numbers; simultaneous diophantine approximations to coordinates of points; product of elliptic curves; measure for algebraic independence; Weierstrass elliptic function Robert Tubbs, A Diophantine problem on elliptic curves, Trans. Amer. Math. Soc. 309 (1988), no. 1, 325 -- 338. Algebraic independence; Gel'fond's method, Elliptic curves A diophantine problem on 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 \(x^n+y^m+1=0\) tensor products of cyclic algebras; division algebras of prime index; division algebras over function fields; cubic divisors; central division algebras; ramification divisors; Brauer groups; exponents Michel Van den Bergh, Division algebras on \?² of odd index, ramified along a smooth elliptic curve are cyclic, Algèbre non commutative, groupes quantiques et invariants (Reims, 1995) Sémin. Congr., vol. 2, Soc. Math. France, Paris, 1997, pp. 43 -- 53 (English, with English and French summaries). Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Brauer groups of schemes Division algebras on \(\mathbb{P}^2\) of odd index, ramified along a smooth elliptic curve are cyclic
| 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 of fields of rational functions on algebraic varieties over number fields; Bloch-Kato conjecture F.\ A. Bogomolov, On two conjectures in birational algebraic geometry, Algebraic geometry and analytic geometry (Tokyo 1990), ICM-90 Satell. Conf. Proc., Springer, Tokyo (1991), 26-52. Algebraic functions and function fields in algebraic geometry, (Co)homology theory in algebraic geometry, Galois cohomology, Rational and birational maps, Varieties over global fields On two conjectures in birational algebraic 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 \(x^n+y^m+1=0\) equidistribution of exponential sums on an arithmetic surface; \({\mathcal D}\)-modules; derived categories; differential algebra in the tannakian category; one-parameter families of exponential sums over finite fields; classical differential equations with polynomial coefficients; \(\ell \)- adic perverse sheaves; differential galois group; rigid GAGA; deformation equations N. M. Katz, \textit{Exponential sums and differential equations}, \textit{Annals of Mathematics Studies}\textbf{124}, Princeton University Press, 1990. Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to field theory, Research exposition (monographs, survey articles) pertaining to number theory, Exponential sums, \(p\)-adic differential equations, Finite ground fields in algebraic geometry, Abstract differential equations Exponential sums and differential equations
| 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; function fields; elliptic surfaces; elliptic divisibility sequences; primitive divisors; Zsigmondy bound Elliptic curves, Elliptic curves over global fields, Special sequences and polynomials, Elliptic surfaces, elliptic or Calabi-Yau fibrations Primitive divisors of sequences associated to 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 \(x^n+y^m+1=0\) birational classification of real rational surfaces; classification of function fields; ruled surface Silhol, R., Classification birationnelle des surfaces rationnelles réelles, 308-324, (1990), Berlin Special surfaces, Topology of real algebraic varieties, Rational and birational maps, Families, moduli, classification: algebraic theory, Arithmetic theory of algebraic function fields Birational classification of real 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 \(x^n+y^m+1=0\) relative homotopy group; locally ringed \(T_ 0\) spaces; elliptic curve; fundamental groups of affine models; homotopy theory internal to algebraic varieties; monoid in algebraic varieties with zero Homotopy groups of special types, Homotopy theory and fundamental groups in algebraic geometry, Elliptic curves, Formal methods and deformations in algebraic geometry Fundamental groups of elliptic curves internal to locally ringed spaces
| 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; Galois group of bitangents; moduli space of plane quartic curves with a flex; Mordell-Weil lattice Shioda, T., Plane quartics and Mordell-Weil lattices of type \(E_7\), Comment. math. univ. st. Pauli, 42, 1, 61-79, (1993) Singularities of curves, local rings, Rational and unirational varieties, Rational points Plane quartics and Mordell-Weil lattices of type \(E_ 7\)
| 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 \(x^n+y^m+1=0\) Dynkin diagrams; normal quartic surfaces; sextic curves; prescribed singularities; action of the Weyl group on the moduli space Urabe, T.: On quartic surfaces and sextic curves with singularities of type \(\tilde E_8 \) ,T 2, 3, 7,E 12. Publ. RIMS, Kyoto Univ.20, 1185-1245 (1984) Singularities of surfaces or higher-dimensional varieties, Singularities of curves, local rings, Special surfaces, Singularities in algebraic geometry On quartic surfaces and sextic curves with singularities of type \(\tilde E_ 8\), \(T_{2,3,7}\), \(E_{12}\)
| 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 \(x^n+y^m+1=0\) functions of a complex variable; holomorphic functions; meromorphic functions; geometric function theory; elliptic functions; elliptic integrals; elliptic curves Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable, Analytic continuation of functions of one complex variable, Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, Meromorphic functions of one complex variable (general theory), Analytic theory of abelian varieties; abelian integrals and differentials Foundations of function theory. An introduction to complex analysis and its applications. For Bachelor and diploma degrees
| 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 fields; elliptic curves; rank; torsion group Aguirre, J., Dujella, A., Jukić Bokun, M., Peral, J.C.: High rank elliptic curves with prescribed torsion group over quadratic fields. Period. Math. Hungar. \textbf{68}, 222-230 (2014) Elliptic curves over global fields, Elliptic curves, Quadratic extensions High rank elliptic curves with prescribed torsion group over quadratic 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 \(x^n+y^m+1=0\) Bibliography; torsion points; L-series; Heegner points; arithmetic of elliptic curves; elliptic curves; elliptic curves over number fields; bibliography Frey, G.: Some aspects of the theory of elliptic curves over number fields. Exposition. math. 4, 35-66 (1986) Special algebraic curves and curves of low genus, Elliptic curves, Arithmetic ground fields for curves Some aspects of the theory 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 \(x^n+y^m+1=0\) Shafarevich-Tate group; Picard groups; transcendental \(j\)-invariant; finite field; algebraic function field; elliptic curve; fibers of the Néron model; irreducible projective curve; Selmer group; embedding Elliptic curves over global fields, Global ground fields in algebraic geometry, Elliptic curves, Arithmetic ground fields for curves Selmer groups and Picard 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 \(x^n+y^m+1=0\) rational points of curves over finite fields; Frobenius sequence; Weil number Arithmetic ground fields for curves, Finite ground fields in algebraic geometry, Rational points, Curves over finite and local fields, Special algebraic curves and curves of low genus Frobenius order-sequences 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 \(x^n+y^m+1=0\) CM cycles; Shimura curves; Abel-Jacobi map in Hodge numbers; abelian surfaces with quaternionic multiplication; complex multiplication cycles; Griffiths group of infinite rank A. Besser, CM cycles over Shimura curves, J. Algebraic Geom. 4 (1995), no. 4, 659-691. Picard groups, Modular and Shimura varieties, Complex multiplication and abelian varieties, Arithmetic aspects of modular and Shimura varieties, Picard schemes, higher Jacobians CM cycles over Shimura 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 \(x^n+y^m+1=0\) family of curves; alterations; group actions de Jong, A. Johan, Families of curves and alterations, Université de Grenoble. Annales de l'Institut Fourier, 47, 599-621, (1997) Families, moduli of curves (algebraic) Families of curves and alterations
| 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 \(x^n+y^m+1=0\) cryptography; finite fields; elliptic curves; authentication; secret sharing; analysis of algorithms Cryptography, Authentication, digital signatures and secret sharing, Finite fields (field-theoretic aspects), Elliptic curves, Analysis of algorithms Threshold ECDSA with an offline recovery party
| 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 variety; cone of curves; Néron-Severi group; cone theorem \beginbarticle \bauthor\binitsT. \bsnmBauer, \batitleOn the cone of curves of an Abelian variety, \bjtitleAmer. J. Math. \bvolume120 (\byear1998), no. \bissue5, page 997-\blpage1006. \endbarticle \OrigBibText T. Bauer. On the cone of curves of an abelian variety. American Journal of Mathematics , 120(5), 1998. \endOrigBibText \bptokstructpyb \endbibitem Isogeny, Algebraic cycles, Plane and space curves, Picard groups On the cone of curves of an abelian variety
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves of genus 4; moduli space; reflection group; K3 surface Shigeyuki Kondō, The moduli space of curves of genus 4 and Deligne-Mostow's complex reflection groups, Algebraic geometry 2000, Azumino (Hotaka), Adv. Stud. Pure Math., vol. 36, Math. Soc. Japan, Tokyo, 2002, pp. 383 -- 400. Families, moduli of curves (analytic), \(K3\) surfaces and Enriques surfaces, Discrete subgroups of Lie groups, Connections of hypergeometric functions with groups and algebras, and related topics, Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), Special algebraic curves and curves of low genus The moduli space of curves of genus 4 and Deligne-Mostow's complex reflection 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 \(x^n+y^m+1=0\) automorphism groups; rational points; maximal curves; function fields Bassa, A.; Ma, L.; Xing, C.; Yeo, S. L., Toward a characterization of subfields of the Deligne-Lusztig function fields, \textit{J. Comb. Theory Ser. A}, 120, 1351-1371, (2013) Combinatorial aspects of representation theory, Curves over finite and local fields, Finite ground fields in algebraic geometry, Automorphisms of curves, Arithmetic theory of algebraic function fields Towards a characterization of subfields of the Deligne-Lusztig 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 \(x^n+y^m+1=0\) Mordell-Weil group of rank at least 19; simple Jacobian; curves of genus 2 Stoll, M., Two simple 2-dimensional abelian varieties defined over \(\mathbb{Q}\) with Mordell-Weil rank at least 19, C. R. Acad. Sci. Paris, Sér. I, 321, 1341-1344, (1995) Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties Two simple 2-dimensional abelian varieties defined over \(\mathbb{Q}\) with Mordell-Weil group of rank at least 19
| 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; bounds for the height of rational points; torsion; canonical height; integral points; elliptic curves Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Heights, Rational points Integral points on elliptic 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 \(x^n+y^m+1=0\) torsion group; elliptic curves; quadratic fields Kamienny, S; Najman, F, Torsion groups of elliptic curves over quadratic fields, Acta. Arith, 152, 291-305, (2012) Elliptic curves over global fields, Elliptic curves Torsion groups of elliptic curves over quadratic 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 \(x^n+y^m+1=0\) canonical automorphisms of order 2; hyperelliptic Shimura curves; rational points Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Global ground fields in algebraic geometry, Rational points Shimura 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 \(x^n+y^m+1=0\) quotient singularities; Gorenstein singularities; canonical bundle; Gorenstein log del Pezzo surface; algebraic compactification of the affine plane; fundamental group M. Miyanishi and D.-Q. Zhang, ''Gorenstein log del Pezzo surfaces of rank one,'' J. Algebra 118(1), 63--84 (1988). Special surfaces, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Coverings in algebraic geometry, Families, moduli, classification: algebraic theory Gorenstein log del Pezzo surfaces of rank one
| 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 the spin moduli spaces of Riemann surfaces with spin structure; Arf invariant; spin mapping class groups; fermionic string theory; Picard group; configuration of simple closed curves on a surface Harer J.L. (1990) Stability of the homology of the moduli spaces of Riemann surfaces with spin structure. Math. Ann. 287(2): 323--334 General low-dimensional topology, Teichmüller theory for Riemann surfaces, Homology of classifying spaces and characteristic classes in algebraic topology, Differential topological aspects of diffeomorphisms, Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Stability of the homology of the moduli spaces of Riemann surfaces with spin structure
| 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 \(x^n+y^m+1=0\) zeta function; Weil system; asymptotically exact family of curves; reciprocal roots of the zeta function; asymptotic Weil measure; asymptotic class number Tsfasman, M. A.; Vlăduţ, S. G., Asymptotic properties of zeta-functions, J. Math. Sci. (N. Y.), 84, 5, 1445-1467, (1997) Curves over finite and local fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Other Dirichlet series and zeta functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Asymptotic properties of zeta-functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finiteness of Tate-Shafarevich-group; modular elliptic curves Modular and Shimura varieties, Elliptic curves The Kolyvagin papers on Weil curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points; Jacobians; curves of higher genus; descent; Mordell-Weil group Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Jacobians, Prym varieties Solving diophantine problems on curves via descent on the Jacobian
| 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 group of automorphisms; Pic; Brauer group; Picard group Galois theory and commutative ring extensions, Morphisms of commutative rings, (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Brauer groups of schemes, Picard groups The seven-term sequence in the Galois theory of rings
| 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 \(x^n+y^m+1=0\) \(F\)-pure threshold; Deuring polynomial; Legendre polynomial; singularities of curves; finite fields Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Computational aspects and applications of commutative rings, Curves over finite and local fields, Computational aspects of algebraic curves, Singularities in algebraic geometry, Elliptic curves over global fields Legendre polynomials roots and the \(F\)-pure threshold of bivariate forms
| 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; pairing-based cryptography; elliptic curves of \(j\)-invariant 1728; Kummer surfaces; rational curves; Weil restriction; isogenies Rational and birational maps, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Isogeny, Elliptic curves Hashing to elliptic curves of \(j\)-invariant 1728
| 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 \(x^n+y^m+1=0\) Calabi-Yau threefolds; fiber product of relatively minimal rational elliptic surfaces with section; automorphisms of rational elliptic surfaces; group actions; non-simply connected Calabi-Yau threefolds; fixed points Automorphisms of surfaces and higher-dimensional varieties, \(3\)-folds, Calabi-Yau manifolds (algebro-geometric aspects), Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces Non-simply connected Calabi-Yau threefolds constructed as quotients of Schoen threefolds
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves over finite fields; Ringel-Hall algebra; coherent sheaves; quantum affine algebras; automorphic forms; Drinfeld double; Heisenberg double M. Kapranov, ''Eisenstein series and quantum affine algebras,'' J. Math. Sci. (New York), vol. 84, iss. 5, pp. 1311-1360, 1997. Relationship to Lie algebras and finite simple groups, Representations of quivers and partially ordered sets, Quantum groups (quantized enveloping algebras) and related deformations Eisenstein series and quantum affine algebras
| 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 \(x^n+y^m+1=0\) coordinate ring of an irreducible affine curve; Pic; Picard group DOI: 10.1007/BF01215648 Picard groups, Singularities of curves, local rings Picard groups of singular affine curves over a perfect 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 \(x^n+y^m+1=0\) Prym varieties; automorphisms of curves Jacobians, Prym varieties, Automorphisms of curves On Prym varieties for the coverings of some singular plane 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 \(x^n+y^m+1=0\) fine moduli space of smooth complex curves; fundamental group; \(n\)-pointed curves Families, moduli of curves (algebraic), Homotopy theory and fundamental groups in algebraic geometry, Coverings of curves, fundamental group The fundamental groups at infinity of the moduli spaces 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 \(x^n+y^m+1=0\) mirror family of cubic curves; Riemann theta function; Ising model Roan, S., Mirror symmetry of elliptic curves and Ising model, J. Geom. Phys., 20, 273-296, (1996) Theta functions and abelian varieties, Equilibrium statistical mechanics Mirror symmetry of elliptic curves and Ising model
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) group of automorphisms of algebraic variety; group of univalent algebraic correspondences Birational automorphisms, Cremona group and generalizations, Rational and birational maps, Automorphisms of surfaces and higher-dimensional varieties One-valued algebraic mappings of the projective plane
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite fields; algebraic curves; Riemann-Roch theorem; number of rational points of an algebraic curves over a finite field; Riemann hypothesis; Hasse-Weil bound; asymptotic problems; zeta-functions and linear systems; a characterization of the Suzuki curve; maximal curves; Hermitian curve; Weierstrass points Torres F.: Algebraic curves with many points over finite fields. In: Martínez-Moro, E., Munuera, C., Ruano, D. (eds) Advances in Algebraic Geometry Codes, pp. 221--256. World Scientific Publishing Company, Singapore (2008) Local ground fields in algebraic geometry, Complex multiplication and moduli of abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Research exposition (monographs, survey articles) pertaining to number theory Algebraic curves with many points 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 \(x^n+y^m+1=0\) rational curves; degenerations of hypersurfaces; Hilbert scheme; Chern class; Segre class; Chow group Formal methods and deformations in algebraic geometry, Hypersurfaces and algebraic geometry, Curves in algebraic geometry, Parametrization (Chow and Hilbert schemes) On limiting rational 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 \(x^n+y^m+1=0\) trigonal curves; algebraic stack; stack of smooth curves; Picard group of a stack; stack of vector bundles on a conic Bolognesi, M; Vistoli, A, Stacks of trigonal curves, Trans. Am. Math. Soc., 364, 3365-3393, (2012) Families, moduli of curves (algebraic), Generalizations (algebraic spaces, stacks), Picard groups Stacks of trigonal 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 \(x^n+y^m+1=0\) Riemann surface; moduli space of semistable vector bundles on curves; non-abelian theta-function; determinant line bundle; theta divisor; trisecant identity Ben-Zvi, David and Biswas, Indranil, Theta functions and {S}zegő kernels, International Mathematics Research Notices, 2003, 24, 1305-1340, (2003) Vector bundles on curves and their moduli, Theta functions and curves; Schottky problem, Families, moduli of curves (algebraic), Theta functions and abelian varieties Theta functions and Szegö 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 \(x^n+y^m+1=0\) division points of Drinfeld modules; arithmetic of function fields; class numbers; cyclotomic function fields; zeta-functions; Teichmüller characters; Artin conjecture; Artin L-series; p-adic measure; Main conjecture of Iwasawa theory; Frobenius; p-class groups; Bernoulli- Carlitz numbers Goss, D.: Analogies between global fields. Canad. math. Soc. conf. Proc. 7, 83-114 (1987) Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Fibonacci and Lucas numbers and polynomials and generalizations, Algebraic functions and function fields in algebraic geometry, Iwasawa theory, Cyclotomic extensions, Zeta functions and \(L\)-functions of number fields Analogies between global 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 \(x^n+y^m+1=0\) Elliptic curves with CM; large algebraic fields; absolute Galois group; Haar measure; class number Elliptic curves over global fields, Field arithmetic, Elliptic curves, Complex multiplication and abelian varieties On the number of elliptic curves with CM over large algebraic 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 \(x^n+y^m+1=0\) complex multiplication; elliptic curves; Hecke characters of imaginary quadratic fields Arithmetic ground fields for curves, Complex multiplication and abelian varieties, Quadratic extensions, Elliptic curves, Special algebraic curves and curves of low genus Une classe de courbes elliptiques à multiplication complexe
| 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 variety; \(abc\)-conjecture; finiteness theorem for \(S\)-unit points of a diophantine equation; Nevanlinna-Cartan theory over function fields Varieties over global fields, Rational points, Diophantine approximation, transcendental number theory, Nevanlinna theory; growth estimates; other inequalities of several complex variables Value distribution theory over function fields and a diophantine equation
| 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 \(x^n+y^m+1=0\) density of integer points; symmetric space; affine variety; volume function; regularizing Eisenstein periods Good, A.: The convolution method for Dirichlet series. In: \textit{The Selberg trace formula and related topics (Brunswick, Maine, 1984)}, volume~53 of \textit{Contemp. Math.}, pages 207-214. Amer. Math. Soc., Providence, RI, (1986) Varieties over global fields, Group actions on varieties or schemes (quotients), Arithmetic varieties and schemes; Arakelov theory; heights, Semisimple Lie groups and their representations, Differential geometry of symmetric spaces Density of integer points on affine homogeneous 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 \(x^n+y^m+1=0\) \(p\)-divisible group; modular elliptic curves; Galois representation; companion form; tame ramification; cuspidal eigenform; Kodaira-Spencer pairing; Serre-Tate pairing; Tate module of the Jacobian; de Rham cohomology of the Igusa curve Robert, F, Coleman and josé felipe voloch, companion forms and Kodaira-spencer theory, Invent. Math., 110, 263-281, (1992) Holomorphic modular forms of integral weight, Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, \(p\)-adic cohomology, crystalline cohomology, Elliptic curves, Formal groups, \(p\)-divisible groups Companion forms and Kodaira-Spencer 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 \(x^n+y^m+1=0\) characteristic p; finite generation of Witt groups of curves; Witt group of a conic Parimala R, Witt groups of conics, elliptic and hyperelliptic curves,J. Number Theory 28 (1988) 69--93 Arithmetic ground fields for curves, General binary quadratic forms, Finite ground fields in algebraic geometry, Local ground fields in algebraic geometry Witt groups of conics, elliptic, and 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 \(x^n+y^m+1=0\) rational points; Néron-Severi group; Jacobian variety; Néron-Tate pairing; number of fixed points; Thue curves; number of integral points Rational points, Jacobians, Prym varieties, Enumerative problems (combinatorial problems) in algebraic geometry, Higher degree equations; Fermat's equation Integral and rational points on algebraic curves of certain types and their Jacobian varieties 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 \(x^n+y^m+1=0\) cubic differential system; configuration of invariant straight lines; multiplicity of an invariant straight line; group action; affine invariant polynomial Guangjian, S., Jifang, S.: The n-degree differential system with \((n-1)(n+1)/2\) straight line solutions has no limit cycles. In: Proc. of Ordinary Differential Equations and Control Theory, Wuhan, pp. 216-220 (1987) \textbf{(in Chinese)} Nonlinear differential equations in abstract spaces, Geometric methods in ordinary differential equations, Group actions on varieties or schemes (quotients), Symmetries, invariants of ordinary differential equations One new class of cubic systems with maximum number of invariant lines omitted in the classification of J. Llibre and N. Vulpe
| 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 \(x^n+y^m+1=0\) Zariski pair; Mordell-Weil group; K3 surfaces; complement of plane curves; Milnor index; Alexander polynomials E Artal Bartolo, H Tokunaga, Zariski pairs of index 19 and Mordell-Weil groups of \(K3\) surfaces, Proc. London Math. Soc. \((3)\) 80 (2000) 127 Plane and space curves, Coverings of curves, fundamental group, \(K3\) surfaces and Enriques surfaces Zariski pairs of index 19 and Mordell-Weil groups of \(K3\) 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 \(x^n+y^m+1=0\) irreducible Galois representations; arithmetic of number fields; division points of elliptic curves; projective vectors; complex Galois representations; automorphic representations; \(\ell -adic\) representation Integral representations related to algebraic numbers; Galois module structure of rings of integers, Galois theory, Elliptic curves, Global ground fields in algebraic geometry, Langlands-Weil conjectures, nonabelian class field theory, Representation-theoretic methods; automorphic representations over local and global fields Projective vectors of complex Galois representations
| 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 \(x^n+y^m+1=0\) crystalline cohomology of modular curves; étale cohomology; \(p\)-divisible group; Shimura curve; Fontaine's conjecture Faltings, Gerd, Crystalline cohomology of semistable curve\textemdash the \({\mathbf Q}_p\)-theory, J. Algebraic Geom., 1056-3911, 6, 1, 1\textendash 18 pp., (1997) \(p\)-adic cohomology, crystalline cohomology, Étale and other Grothendieck topologies and (co)homologies, Arithmetic ground fields for curves, Modular and Shimura varieties Crystalline cohomology of semistable curve -- the \(\mathbb{Q}_ p\)-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 \(x^n+y^m+1=0\) finite fields; algebraic curves; upper bound; number of rational points Hirschfeld, J. W.P.; Korchmáros, G., On the number of rational points on an algebraic curve over a finite field, Bull. Belg. Math. Soc. Simon Stevin, 5, 313-340, (1998) Curves over finite and local fields, Rational points, Finite ground fields in algebraic geometry, Arithmetic ground fields for curves, Blocking sets, ovals, \(k\)-arcs On the number of rational points on an algebraic curve 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 \(x^n+y^m+1=0\) elliptic curves; j-invariant; modular curves; function fields Ishii, Noburo, Rational expression for \(j\)-invariant function in terms of generators of modular function fields, Int. Math. Forum, 2, 37-40, 1877-1894, (2007) Elliptic curves over global fields, Elliptic curves Rational expression for \(j\)-invariant function in terms of generators of modular 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 variety; set of non-proper points; parametric curves; \( \mathbb{K} \)-uniruled set; degree of \(\mathbb{K} \)-uniruledness; positive characteristic Affine fibrations Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case
| 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 action; stack; algebraic stack; quotient stack; moduli space of curves Matthieu Romagny, ''Group actions on stacks and applications'', Mich. Math. J.53 (2005) no. 1, p. 209-236 Generalizations (algebraic spaces, stacks), Families, moduli of curves (algebraic), Automorphisms of curves, Coverings of curves, fundamental group Group actions on stacks and 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 \(x^n+y^m+1=0\) galois automorphisms; fundamental group of the projective line minus three points Hiroaki Nakamura, On Galois automorphisms of the fundamental group of the projective line minus three points, Math. Z. 206 (1991), no. 4, 617 -- 622. Coverings of curves, fundamental group, Galois theory, Global ground fields in algebraic geometry, Coverings in algebraic geometry On galois automorphisms of the fundamental group of the projective line minus three points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quadratic form; function field of a quadric; unramified Witt group; Galois cohomology; stable birational equivalence B. Kahn and A. Laghribi, A second descent problem for quadratic forms, K-Theory 29 (2003), 253--284. Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Galois cohomology, Motivic cohomology; motivic homotopy theory A second descent problem for quadratic forms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) representations of a dicrete group in \(SL_ 2({\mathbb{C}})\); actions on generalized trees; hyperbolic structures on surfaces; varieties of group representations; compactification of Teichmüller space; compactifications of real and complex algebraic varieties; affine algebraic set; valuations of the coordinate ring J. Morgan, P. Shalen. Valuations, trees, and degenerations of hyperbolic structures. I, \textit{Ann. of Math. } 120 (1984), 401--476. General low-dimensional topology, Abelian varieties and schemes, Valuations and their generalizations for commutative rings, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Compactification of analytic spaces, Group rings of finite groups and their modules (group-theoretic aspects), Classification theory of Riemann surfaces Valuations, trees, and degenerations of hyperbolic structures. I
| 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 \(x^n+y^m+1=0\) Picard group; Tamagawa number; Brauer-Manin obstruction; Zbl 0991.72285; asymptotic behaviour; counting function; number of rational points of bounded height; Fano variety; geometric invariants; diagonal cubic surfaces; algorithm Peyre, E.; Tschinkel, Y., \textit{Tamagawa numbers of diagonal cubic surfaces, numerical evidence}, Math. Comp., 70, 367-387, (2001) Rational points, Fano varieties, Heights, Cubic and quartic Diophantine equations, Arithmetic varieties and schemes; Arakelov theory; heights Tamagawa numbers of diagonal cubic surfaces, numerical evidence
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms of an affine surface; weighted degree of automorphisms Polynomial rings and ideals; rings of integer-valued polynomials, Birational automorphisms, Cremona group and generalizations, Automorphisms of surfaces and higher-dimensional varieties, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) On weighted degree for polynomial rings
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fields of real algebraic functions; reduced Whitehead group; Hasse principle; norm mapping Class field theory, Algebraic functions and function fields in algebraic geometry, \(K\)-theory of global fields, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Finite-dimensional division rings, Grothendieck groups, \(K\)-theory, etc. Norms in fields of real algebraic functions, and the reduced Whitehead 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 \(x^n+y^m+1=0\) sheaf of regular functions; first cohomology group; algebraically closed fields Polynomials in general fields (irreducibility, etc.), Elementary questions in algebraic geometry, Other nonalgebraically closed ground fields in algebraic geometry, Real algebraic and real-analytic geometry A note on cohomology over non algebraically closed 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 \(x^n+y^m+1=0\) weak approximation property; Brauer-Manin obstruction; abelian varieties; Tate-Shafarevich group; elliptic curves over quadratic fields L. Wang, ''Brauer-Manin obstruction to weak approximation on abelian varieties,'' Israel J. Math., vol. 94, pp. 189-200, 1996. Arithmetic ground fields for abelian varieties, Local cohomology and algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry) Brauer-Manin obstruction to weak approximation on abelian 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 \(x^n+y^m+1=0\) étale cohomology; crystalline cohomology; period map; Tate-module of a \(p\)-divisible group; differentials; elliptic curves CREW (R.) . - Universal extensions and p-adic periods of elliptic curves , Compositio Math., t. 73, 1990 , p. 107-119. Numdam | MR 91k:11045 | Zbl 0742.14013 \(p\)-adic cohomology, crystalline cohomology, Elliptic curves, Period matrices, variation of Hodge structure; degenerations, Arithmetic ground fields for curves, Étale and other Grothendieck topologies and (co)homologies, Formal groups, \(p\)-divisible groups Universal extensions and \(p\)-adic periods of elliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic stacks; intersection theory of moduli spaces of curves; KdV equation; tau-function; matrix integral; cellular decomposition of the moduli space; intersection numbers; trivalent graphs; stable ribbon graphs Terasoma, T.: Fundamental groups of moduli spaces of hyperplane configurations. http://gauss.ms.u-tokyo.ac.jp/paper/paper.html Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Families, moduli of curves (algebraic), Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, KdV equations (Korteweg-de Vries equations) Witten's intersection theory of moduli spaces of curves (After Kontsevich)
| 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; affine varieties; finite fields; complete intersection; exponential sums; asymptotic formula; upper estimate; number of integral points \beginbarticle \bauthor\binitsW. \bsnmLuo, \batitleRational points on complete intersections over \(\F_p\), \bjtitleInt. Math. Res. Not. IMRN \bvolume1999 (\byear1999), page 901-\blpage907. \endbarticle \OrigBibText W. Luo, Rational points on complete intersections over \(\F_p\), Inter. Math. Res. Notices , 1999 (1999), 901-907. \endOrigBibText \bptokstructpyb \endbibitem Varieties over finite and local fields, Finite ground fields in algebraic geometry, Varieties over global fields Rational points on complete intersections over \(F_p\)
| 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 \(x^n+y^m+1=0\) local fields; local class field theory; Dedekind rings; different; discriminant; ramification groups; cyclotomic fields; Hasse's norm theory; cohomology of groups; Galois cohomology; Brauer group; class formation Serre, J.-P., Corps locaux, Actualités Sci. Indust., vol. 1296, (1962), Hermann Algebraic number theory: local fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic problems in algebraic geometry; Diophantine geometry, Class field theory; \(p\)-adic formal groups, Cohomology of groups, Galois cohomology Local fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) supersingular curves; irreducible polynomials; prescribed coefficients; binary fields; characteristic polynomial of Frobenius Ahmadi, Omran; Göloğlu, Faruk; Granger, Robert; McGuire, Gary; Yilmaz, Emrah Sercan, Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients, Finite Fields Appl., 42, 128-164, (2016) Arithmetic ground fields for curves Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients
| 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 \(x^n+y^m+1=0\) supersingular elliptic curves over finite fields; Weierstrass equation; number of rational points F. Morain, Classes d'isomorphismes des courbes elliptiques supersingulières en caracteristique . Util. Math. 52, 241--253 (1997) Elliptic curves over local fields, Curves over finite and local fields, Elliptic curves, Finite ground fields in algebraic geometry Isomorphism classes of supersingular elliptic curves of characteristic \(\geq 3\)
| 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 \(x^n+y^m+1=0\) singular primes in function fields; extension of field of constants; genus Stöhr, K-O, On singular primes in function fields, Arch. Math., 50, 156-163, (1988) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On singular primes 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 \(x^n+y^m+1=0\) Shimura reciprocity law; arithmetic elliptic function field; automorphism group; Jacobi function of level N; Jacobi forms Arithmetic theory of algebraic function fields, Theta series; Weil representation; theta correspondences, Arithmetic ground fields (finite, local, global) and families or fibrations, Automorphic functions in symmetric domains La loi de réciprocité de Shimura pour les fonctions de Jacobi
| 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 \(x^n+y^m+1=0\) polynomial equations of genus zero and one; function field; algorithms; effective determination; diophantine equations in two unknowns; Thue equations; hyperelliptic equations; fundamental inequality; fields of positive characteristic; explicit bounds; solutions in rational functions; superelliptic equations R. C. Mason, \textit{Diophantine Equations over Function Fields.} London Mathematical Society Lecture Note Series, Vol. 96. Cambridge Univ. Press, Cambridge, 1984. \(p\)-adic and power series fields, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic theory of algebraic function fields, Exponential Diophantine equations, Diophantine equations, Approximation to algebraic numbers, Higher degree equations; Fermat's equation, Rational points Diophantine equations 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 \(x^n+y^m+1=0\) Richelot isogenies; superspecial abelian surfaces; reduced group of automorphisms; genus-2 isogeny cryptography Isogeny, Applications to coding theory and cryptography of arithmetic geometry, Automorphisms of curves, Jacobians, Prym varieties Counting superspecial Richelot isogenies by reduced automorphism 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 \(x^n+y^m+1=0\) braid monodromy factorizations; branch curves; fundamental group; invariant of a surface Mina Teicher, New invariants for surfaces, Tel Aviv Topology Conference: Rothenberg Festschrift (1998), Contemp. Math., vol. 231, Amer. Math. Soc., Providence, RI, 1999, pp. 271 -- 281. Homotopy theory and fundamental groups in algebraic geometry, Braid groups; Artin groups, Families, moduli, classification: algebraic theory New invariants for 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 \(x^n+y^m+1=0\) survey of the group law algorithms; generalized Jacobian; hyperelliptic curves; cryptography; Arita-Miura-Sekiguchi algorithm Applications to coding theory and cryptography of arithmetic geometry, Finite ground fields in algebraic geometry, Jacobians, Prym varieties, Cryptography Group law algorithms for Jacobian varieties 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 \(x^n+y^m+1=0\) Jacobians; linear systems on curves; rank of the Néron-Severi group Picard groups, Divisors, linear systems, invertible sheaves, Jacobians, Prym varieties On the Néron-Severi groups of the surface of special divisors
| 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 \(x^n+y^m+1=0\) postulation; arithmetically Cohen-Macaulay space curve; complete intersection; numerically subcanonical curves; Hilbert function of a general hyperplane section Plane and space curves, Projective techniques in algebraic geometry, Complete intersections Complements to a theorem of Gherardelli: The postulational viewpoint
| 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 \(x^n+y^m+1=0\) polylogarithm; motivic Galois group; Zagier conjecture; mixed Tate category; mixed motivic Tate sheaves; \(K\)-theory; fiber functor; Beilinson-Soulé conjecture; Milnor \(K\)-theory; value of the Dedekind zeta-function at integer points A.B. Goncharov, \textit{Polylogarithms and motivic Galois group}, Proceedings of the Symposium on Pure Mathematics 55, American Mathematical Society, Providence U.S.A. (1994). \(K\)-theory of global fields, (Co)homology theory in algebraic geometry, Higher algebraic \(K\)-theory Polylogarithms and motivic 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 \(x^n+y^m+1=0\) semisimple Lie group; representation of the fundamental group; Higgs bundle; moduli space; Hermitian symmetric space; Morse function Bradlow, S. B.; García-Prada, O.; Gothen, P. B., Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces, Geom. Dedic., 122, 185-213, (2006) Vector bundles on curves and their moduli, Complex-analytic moduli problems, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Applications of global analysis to structures on manifolds, Moduli problems for topological structures Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
| 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; rational places; existence of algebraic function fields; Abelian extensions; different [F-P-S] G. Frey, M. Perret and H. Stichtenoth,On the different of Abelian extensions of global fields, inCoding Theory and Algebraic Geometry (H. Stichtenoth and M. Tsfasman, eds.), Proceedings AGCT3, Luminy June 1991, Lecture Notes in Mathematics1518, Springer, Heidelberg, 1992, pp. 26--32. Arithmetic theory of algebraic function fields, Class field theory, Other abelian and metabelian extensions, Algebraic functions and function fields in algebraic geometry On the different of Abelian extensions of global 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 curves; geometric Goppa codes; algebraic function fields; Skorobogatov-Vladut decoding algorithm; Riemann-Roch theorem; asymptotic Gilbert bound Pretzel O.: Codes and Algebraic Curves. Oxford Lecture Series in Mathematics and Its Applications, vol. 8. The Clarendon Press/Oxford University Press, New York (1998). Combinatorial codes, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Curves over finite and local fields, Arithmetic ground fields for curves, Valuation rings, Field extensions, Algebraic coding theory; cryptography (number-theoretic aspects) Codes and algebraic curves
| 0 |
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