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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 \(x^n+y^m+1=0\) automatic sequences; formal power series; algebraic curves; finite fields Automata sequences, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Automatic sequences and 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 \(x^n+y^m+1=0\) curves with many points; algebraic function fields Rational points, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry On fibre products of Kummer curves with many rational 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 \(x^n+y^m+1=0\) open Riemann surfaces; Teichmüller space; Abelian differentials; period matrices; normal behavior; quasiconformal deformations Y. KUSUNOKI AND F. MAITANI, Variations of abelian differentials under quasi-conformal deformations, Math. Z., 181 (1982), 435-450. Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Period matrices, variation of Hodge structure; degenerations, Differentials on Riemann surfaces, Algebraic functions and function fields in algebraic geometry Variations of Abelian differentials under quasiconformal deformations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) central points; model class of fields; valuation; function field Bröcker, L.; Schülting, H. W.: Valuation theory from the geometrical point of view. J. reine angew. Math. 365, 12-32 (1986) Model theory of fields, Valued fields, Algebraic functions and function fields in algebraic geometry, Model-theoretic algebra Valuations of function fields from the geometrical point of view
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) invariants; covariants; hyperelliptic curves; binary forms; Galois descent; isomorphism; moduli; algorithm Lercier, R.; Ritzenthaler, C.; Sijsling, J., Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent, (ANTS X--Proceedings of the Tenth Algorithmic Number Theory Symposium. ANTS X--Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Ser., vol. 1, (2013), Math. Sci. Publ.: Math. Sci. Publ. Berkeley, CA), 463-486 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic curves, Special algebraic curves and curves of low genus Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) [7]I. Cascudo, R. Cramer and C. Xing, Torsion limits and Riemann--Roch systems for function fields and applications, IEEE Trans. Information Theory 60 (2014), 3871--3888. Algebraic functions and function fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Combinatorial codes Torsion limits and Riemann-Roch systems for function fields 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 \(x^n+y^m+1=0\) higher reciprocity law; modular functions of weight one; elliptic curves; 2-torsion M. Koike, ''Higher reciprocity law, modular forms of weight 1, and elliptic curves,''Nagoya Math. J.,98, 109--115 (1985). Langlands-Weil conjectures, nonabelian class field theory, Holomorphic modular forms of integral weight, Galois representations, Algebraic functions and function fields in algebraic geometry Higher reciprocity law, modular forms of weight 1 and elliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fundamental groups; algebraic curves; Galois representations; stability property; stable derivation algebra Pollack, A.: Relations between derivations arising from modular forms, Ph.D. thesis. Duke University (2009) Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Curves of arbitrary genus or genus \(\ne 1\) over global fields The stable derivation algebras for higher genera
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) regularity index; truncation; analytic type; Milnor number J. Elias , On the analytic equivalence of curves . Proc. Camb. Phil. Soc. 100, 1, 57-64 (1986). Algebraic functions and function fields in algebraic geometry On the analytic equivalence 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 \(x^n+y^m+1=0\) Hilbert irreducibility theorem; height function; algebraic curve Other number fields, Hilbertian fields; Hilbert's irreducibility theorem, Algebraic functions and function fields in algebraic geometry Counting number fields in fibers (with an appendix by Jean Gillibert)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weierstrass points; higher-order Weierstrass points; superelliptic curves; branch points; numerical semigroups Shor, Caleb M., Higher-order Weierstrass weights of branch points on superelliptic curves, (Malmendier, A.; Shaska, T., Algebraic curves and their fibrations in mathematical physics and arithmetic geometry, Contemp. math., (2017), Amer. Math. Soc.), to appear Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields Higher-order Weierstrass weights of branch points on superelliptic 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 \(x^n+y^m+1=0\) quartic Diophantine equations; computation of Selmer group; Jacobian of a curve; algorithms; Mordell-Weil ranks E. Schaefer, ''Computing a Selmer Group of a Jacobian Using Functions on the Curve,'' Math. Ann. 310, 447--471 (1998); ''Erratum,'' Math. Ann. 339, 1 (2007). Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Cubic and quartic Diophantine equations Computing a Selmer group of a Jacobian using functions on the curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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, Other nonalgebraically closed ground fields in algebraic geometry, Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Fibrations, degenerations in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Maps between classifying spaces in algebraic topology, Stacks and moduli problems, Representation theory for linear algebraic groups Remarks on rational points of universal 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 \(x^n+y^m+1=0\) genus 2 curves; rational torsion points; family of curves Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Rational torsion of \(J_0(N)\) for hyperelliptic modular curves and families of Jacobians of genus 2 and genus 3 curves with a rational point of order 5, 7 or 10
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) conic bundle surfaces; Henselian fields; quaternion algebras Finite-dimensional division rings, Forms over real fields, Quadratic forms over general fields, Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Rational and ruled surfaces Note on conic bundles over Henselian discrete valued fields with real closed residue 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 \(x^n+y^m+1=0\) Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group, Automorphisms of curves Correction to ``The automorphism group of a cyclic \(p\)-gonal curve''
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) monster group; modular polynomial; coefficients; \(j\)-invariants of supersingular elliptic curves Modular and automorphic functions, Fourier coefficients of automorphic forms, Algebraic functions and function fields in algebraic geometry On Ito's observation on coefficients of the modular polynomial
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Newton-Puiseux expansions; Jacobian conjecture Abhyankar, S. S., Some remarks on the Jacobian conjecture, \textit{Proc. Indian Acad. Sci. (Math. Sci.)}, 104, 3, 515-542, (1994) Polynomial rings and ideals; rings of integer-valued polynomials, Algebraic functions and function fields in algebraic geometry Some remarks on the Jacobian question. (Notes by Marius van der Put and William Heinzer, updated by Avinash Sathaye)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; function field; Riemann surface; symmetric permutation; group; punctured spheres; moduli spaces Riemann surfaces; Weierstrass points; gap sequences, Separable extensions, Galois theory, Compact Riemann surfaces and uniformization, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group Galois theory and the uniformization of Riemann 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 \(x^n+y^m+1=0\) automorphic form; Drinfeld's shtuka; global function field; Langlands conjecture; moduli stack of shtukas Laumon, G., La correspondance de Langlands sur LES corps de fonctions (d'après Laurent lafforgue), No. 276, 207-265, (2002) Langlands-Weil conjectures, nonabelian class field theory, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Modular forms associated to Drinfel'd modules, Algebraic moduli problems, moduli of vector bundles, Representation-theoretic methods; automorphic representations over local and global fields The Langlands correspondence for function fields (after Laurent Lafforgue)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; constant reduction; valuation prolongation; geometric family; Skolem property; principal family; birational characterization of arithmetic surfaces B. Green, Geometric families of constant reductions and the Skolem property, Trans. Amer. Math. Soc. 350 (1998), no. 4, 1379-1393. Valued fields, Arithmetic theory of algebraic function fields, Arithmetic ground fields for surfaces or higher-dimensional varieties, Global ground fields in algebraic geometry Geometric families of constant reductions and the Skolem property
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 of curves over finite fields; many rational points; maximal function fields R. Fuhrmann and F. Torres. The genus of curves over finite fields with many rational points. Manuscripta Math., 89(1) (1996), 103--106. Curves over finite and local fields, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Arithmetic ground fields for curves The genus of curves over finite fields with many rational points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Pierre de Fermat; René Descartes; Leonhard Euler; affine space; barycenter; real affine space; Pasch's theorem; Euclidean space; metric space; Gram-Schmidt process; approximation by the law of least squares; Fourier approximation; Hermitian space; projective space; duality principle; Fano's theorem; projective quadric; Pascal's theorem; Brianchon's theorem; topology of projective real spaces; algebraic plane curves; Bezout's theorem; Hessian curve; Cramer's paradox; group of a cubic; rational algebraic plane curve; Taylor's formula for polynomials in one or more variables; Eisenstein's criterion; Euler's formula; fundamental theorem of algebra; Sylvester's theorem Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry, General histories, source books, Linear incidence geometric structures with parallelism, Affine analytic geometry, Projective analytic geometry, Euclidean analytic geometry, Questions of classical algebraic geometry, Algebraic functions and function fields in algebraic geometry, Projective techniques in algebraic geometry An algebraic approach to geometry. Geometric trilogy II
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hilbert's tenth Problem; Undecidability; Elliptic curves; Quadratic forms; Rational points; Diophantine model Eisenträger, K., Hilbert's tenth problem for function fields of varieties over number fields and p-adic fields, J. Algebra, 310, 775-792, (2007) Decidability (number-theoretic aspects), Basic properties of first-order languages and structures, Rational points, Arithmetic theory of algebraic function fields Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic 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 \(x^n+y^m+1=0\) field extension; valuation ring; ultrapower Popescu, D.: On Zariski's uniformization theorem. Lect. notes in math. 1056 (1984) Applications of logic to commutative algebra, Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.), Arithmetic theory of algebraic function fields, Valuation rings, Field extensions, Principal ideal rings, Relevant commutative algebra On Zariski's uniformization theorem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 modular functions; function field; higher level; Jacobi functions; Shimura reciprocity law Berndt, Rolf, Sur l'arithmétique du corps des fonctions elliptiques de niveau~{\(N\)}, Seminar on Number Theory, {P}aris 1982--83 ({P}aris, 1982/1983), Progr. Math., 51, 21-32, (1984), Birkhäuser Boston, Boston, MA Modular and automorphic functions, Jacobi forms, Arithmetic theory of algebraic function fields, Homogeneous spaces and generalizations, General theory of automorphic functions of several complex variables On the arithmetic of the elliptic function field of level \(N\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; Galois theory of function fields; Kummer theory; valuations; flag functions F.\ A. Bogomolov and Y. Tschinkel, Commuting elements of Galois groups of function fields, Motives, polylogarithms and Hodge theory. Part I (Irvine 1998), Int. Press Lect. Ser. 3, International Press, Somerville (2002), 75-120. Arithmetic theory of algebraic function fields, Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Configurations and arrangements of linear subspaces Commuting elements in Galois groups of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) periods of hyperelliptic Riemann surfaces Algebraic functions and function fields in algebraic geometry, Period matrices, variation of Hodge structure; degenerations, Classification theory of Riemann surfaces The Neumann problem and equations defining period matrices of hyperelliptic Riemann 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 \(x^n+y^m+1=0\) height theory; families of abelian varieties; relative Bogomolov conjecture; uniform Mordell-Lang Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Rational points, Global ground fields in algebraic geometry A consequence of the relative Bogomolov conjecture
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field; absolutely integral curve Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory On stabilizers of algebraic function fields of one variable
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) conjecture of Grothendieck; full set of algebraic solutions; DFG \(p\)-adic differential equations, Algebraic functions and function fields in algebraic geometry, Local deformation theory, Artin approximation, etc., Local ground fields in algebraic geometry Differential equations which come from 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 \(x^n+y^m+1=0\) Transformations of equations Algebraic functions and function fields in algebraic geometry On the transformation of the equation \(y^n=R(x)\), \(R\) denoting an integral rational function of the variable \(x\) into the equation \(\eta^2=R_1(x)\).
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Arithmetic theory of algebraic function fields, Rational points Generalizations of Golod-Shafarevich 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 \(x^n+y^m+1=0\) finite field; tensor rank of multiplication; function field Number-theoretic algorithms; complexity, Analysis of algorithms and problem complexity, Algebraic functions and function fields in algebraic geometry, Finite fields (field-theoretic aspects) On the tensor rank of multiplication in finite extensions of finite fields and related issues in 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 \(x^n+y^m+1=0\) exponentiation; Parshin completion; maximal flag; Goss zeta function; higher dimensional varieties; ample divisor Kapranov, M.: A higher-dimensional generalization of the goss zeta function. J. number theory 50, 363-375 (1995) Arithmetic theory of algebraic function fields, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of polynomial rings over finite fields, Varieties over finite and local fields, Finite ground fields in algebraic geometry A higher-dimensional generalization of the Goss zeta function
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(\mathbb Z_4\)-code; difference set; planar function; projective plane; semifield; finite field; algebraic curve K.-U. Schmidt, Y. Zhou, Planar functions over fields of characteristic two. \textit{J. Algebraic Combin}. \textbf{40} (2014), 503-526. MR3239294 Zbl 1319.51008 Finite affine and projective planes (geometric aspects), Linear codes (general theory), Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.), Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry Planar functions over fields of characteristic two
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; integral points; curves; arithmetic discriminant; Arakelov theory; Castelnuovo's inequality A. Levin, Vojta's inequality and rational and integral points of bounded degree on curves, Compos. Math. 143 (2007), no. 1, 73-81. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves Vojta's inequality and rational and integral points of bounded degree on curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of primitive points; elliptic curves over number fields Voloch, J. F.: Primitive points on constant elliptic curves over function fields. Bol. soc. Bras. mat. 21, No. 1, 91-94 (1990) Elliptic curves, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Primitive points on constant 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 \(x^n+y^m+1=0\) vanishing cycles; function fields Arithmetic theory of algebraic function fields, Zeta and \(L\)-functions in characteristic \(p\), Structure of families (Picard-Lefschetz, monodromy, etc.) Singularities and vanishing cycles in number theory 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 \(x^n+y^m+1=0\) Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic cycles, Local ground fields in algebraic geometry, Global ground fields in algebraic geometry, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) Arithmetic of \(p\)-adic curves and sections of geometrically abelian fundamental 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 \(x^n+y^m+1=0\) hyperelliptic modular curve; hyperelliptic involution; computation of rational polynomials; modular invariant; number of \(\mathbb{Q}\)-rational points T. Hibino and N. Murabayashi: Modular equations of hyperelliptic \(X_0(N)\) and an application , Acta Arith. 82 (1997), 279--291. Holomorphic modular forms of integral weight, Special algebraic curves and curves of low genus, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields Modular equations of hyperelliptic \(X_0(N)\) and an application
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) descent; Jacobian; hyperelliptic; Selmer group; Magma; explicit algorithm Stoll, M., \textit{implementing 2-descent for Jacobians of hyperelliptic curves}, Acta Arithmetica, XCVIII.3, 245-277, (2001) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for curves, Jacobians, Prym varieties, Number-theoretic algorithms; complexity, Computational aspects of algebraic curves Implementing 2-descent for Jacobians of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cubic points; modular curves; Petri model Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Families, moduli of curves (algebraic), Arithmetic ground fields for curves Infinitely many cubic points for \(X_0^+(N)\) 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 \(x^n+y^m+1=0\) function field of transcendence degree 1; divisors; Riemann-Roch theorem Riemann-Roch theorems, Divisors, linear systems, invertible sheaves, Algebraic functions and function fields in algebraic geometry On the Riemann-Roch theorem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curve; local symbols; reciprocity laws Group schemes, Symbols, presentations and stability of \(K_2\), Algebraic functions and function fields in algebraic geometry An algebraic-geometric method for constructing generalized local symbols on curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational functions Kashiwara, H., Fonctions rationnelles de type (0, 1) sur le plan projectif complexe, Osaka J. Math.,, 24, 521-577, (1987) Algebraic functions and function fields in algebraic geometry, Projective techniques in algebraic geometry, Meromorphic functions of several complex variables Fonctions rationnelles de type (0,1) sur le plan projectif complexe. (Rational functions of (0,1)-type on the complex 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 \(x^n+y^m+1=0\) algebraic geometry T. Kodama, Note on Functional Divisors of Algebraic Function Fields of one Variable. Mem. Fac. Sc., Kyushu Univ., Ser. A19, No. 2, 61--66 (1965). Algebraic functions and function fields in algebraic geometry Note on functional divisors of algebraic function fields of one variable
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(\ell\)-adic representation; abelian varieties; monodromy [3]S. Arias-de-Reyna, W. Gajda, and S. Petersen, Big monodromy theorem for abelian varieties over finitely generated fields, J. Pure Appl. Algebra 217 (2013), 218--229. Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for abelian varieties Big monodromy theorem for abelian varieties over finitely generated 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 \(x^n+y^m+1=0\) modular curves; optimal towers; algebraic-geometric codes Li, W. -C.W.: Modularity of asymptotically optimal towers of function fields. Coding, cryptography and combinatorics, 51-65 (2004) Applications to coding theory and cryptography of arithmetic geometry, Rational points, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic theory of algebraic function fields Modularity of asymptotically optimal towers of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(p\)-adic integration; Jacobian McCallum, William; Poonen, Bjorn, The method of Chabauty and Coleman, explicit methods in number theory, Panor. Synthèses, vol. 36, 99-117, (2012), Soc. Math. France Paris, (English, with English and French summaries), MR3098132 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Analytic theory of abelian varieties; abelian integrals and differentials The method of Chabauty and Coleman
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; universal Jacobians; hyperelliptic curves; compactifications of moduli spaces; line bundles on hyperelliptic curves Generalizations (algebraic spaces, stacks), Picard groups, Algebraic moduli problems, moduli of vector bundles, Algebraic functions and function fields in algebraic geometry Gauss composition for \(\mathbb{P}^1\), and the universal Jacobian of the Hurwitz space of double covers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algorithm; divisor reduction F. Heß, Computing Riemann--Roch spaces in algebraic function fields and related topics. J. Symb. Comput. 33, 425--445 (2002) Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry, Riemann-Roch theorems, Software, source code, etc. for problems pertaining to algebraic geometry Computing Riemann-Roch spaces in algebraic function fields and related topics.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) triangular Shimura curves; modular groups; discriminant; cocompact arithmetic triangle groups; automorphic function Modular and automorphic functions, Structure of modular groups and generalizations; arithmetic groups, Automorphic forms, one variable, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Analogs of \(\Delta (z)\) for triangular 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 \(x^n+y^m+1=0\) Chevalley-Weil theorem; projective curves; unramified map Dedekind, R.: Gesammelte mathematische Werke. Bände I-III. Herausgegeben von Robert Fricke, Emmy Noether und Öystein Ore. Chelsea Publishing Co., New York (1968) Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields An effective version of Chevalley-Weil theorem for projective 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 \(x^n+y^m+1=0\) complex multipliction; isogenous Jacobian; real multiplication; rational function field; hyperelliptic curves Mestre, J. F.: Courbes hyperelliptiques à multiplications réelles. C. R. Acad. sci. Paris, ser. I math. 307, 721-724 (1988) Elliptic curves, Algebraic functions and function fields in algebraic geometry, Complex multiplication and abelian varieties, Galois theory Courbes hyperelliptiques à multiplications réelles. (Hyperelliptic curves with real multiplications)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic function; Series expansion; Coefficient; Prime factor Algebraic functions and function fields in algebraic geometry, Power series (including lacunary series) in one complex variable On a theorem of Eisenstein.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curves; Jacobian; arithmetic invariant theory; line bundles Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves A remark on the arithmetic invariant theory of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic functions and function fields in algebraic geometry Zur Theorie der algebraischen Functionen.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curves; isogeny; Jacobians Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Isogeny 2-2-2 isogenies between Jacobians of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) deformations of Klein curve; group of automorphisms; deformations of Riemann surfaces; Torelli theorem; abelian differentials; Hodge decomposition; geodesics; quadratic differentials Algebraic functions and function fields in algebraic geometry, Differentials on Riemann surfaces, Transcendental methods, Hodge theory (algebro-geometric aspects), Fuchsian groups and their generalizations (group-theoretic aspects), Analytic theory of abelian varieties; abelian integrals and differentials, Families, moduli of curves (analytic), Complex Lie groups, group actions on complex spaces Deformations of Klein's curve and representations of its group of 168 automorphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois points; plane curve; dual curve Plane and space curves, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Galois points for a plane curve and its dual curve. II.
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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Burkhardt quartic threefold; Hesse pencil Abelian varieties of dimension \(> 1\), Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Families, moduli of curves (algebraic), Algebraic moduli of abelian varieties, classification Arithmetic aspects of the Burkhardt quartic threefold
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Diophantine equations; Bogomolov-Miyaoka inequality; arithmetic surfaces; small point conjecture; effective Mordell conjecture; Szpiro conjecture; branched coverings of curves; asymptotic Fermat theorem; abc-conjecture; height; effectivity Moret-Bailly, L., Hauteurs et classes de Chern sur LES surfaces arithmétiques, Astérisque, 183, 37-58, (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves, Arithmetic ground fields for surfaces or higher-dimensional varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields Heights and Chern classes on arithmetic 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 \(x^n+y^m+1=0\) algebraic groups; Abelian varieties; elliptic curves; algebraic differentials; generalized Albanese variety Faltings, G; Wüstholz, G, Einbettungen kommutativer algebraischer gruppen und einige eigenschaften, J. Reine Angew. Math., 354, 175-205, (1984) Group varieties, Transcendence (general theory), Algebraic functions and function fields in algebraic geometry, Elliptic curves Einbettungen kommutativer algebraischer Gruppen und einige ihrer Eigenschaften
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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 \(x^n+y^m+1=0\) differentials of the first kind; quadratic transformations Algebraic functions and function fields in algebraic geometry On a point in the theory of abelian 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 \(x^n+y^m+1=0\) Bogomolov, F., Tschinkel, Yu.: Couniformization of curves over number fields. In: Bogomolov, F., Tschinkel, Yu. (eds.) Geometric Methods in Algebra and Number Theory. Progress in Mathematics, vol.~235, pp.~43-57. Birkhäuser, Boston (2005). http://www.math.nyu.edu/~tschinke/papers/yuri/04covers/cover4.pdf Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields Couniformization of curves over number fields
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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves of genus two; Jacobians; canonical height; infinite descent; Mordell-Weil group; algorithm E.V. Flynn and N.P. Smart, Canonical heights on the Jacobians of curves of genus 2 and the infinite descent, Acta Arith., 79 (1997), 333-352. MR 98f:11066 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
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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 \(x^n+y^m+1=0\) stable reduction of curves; completely valued fields; ultrametric valuation; topological function field; topological genus; inequalities Non-Archimedean valued fields, Algebraic functions and function fields in algebraic geometry Genre topologique des corps valués. (Topological genus of valued 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 \(x^n+y^m+1=0\) ruled function fields; Zariski problem; finitely generated extensions; automorphisms James K. Deveney, Automorphism groups of ruled function fields and a problem of Zariski, Proc. Amer. Math. Soc. 90 (1984), no. 2, 178 -- 180. Transcendental field extensions, Algebraic functions and function fields in algebraic geometry Automorphism groups of ruled function fields and a problem of Zariski
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Arakelov theory; arithmetic surfaces; compact Riemann surfaces; moduli spaces; Riemann-Roch theorems; hyperbolic geometry; modular forms Arithmetic varieties and schemes; Arakelov theory; heights, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (analytic), Curves of arbitrary genus or genus \(\ne 1\) over global fields \(\Omega\)-admissible 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 \(x^n+y^m+1=0\) effective divisors; families of sheaves; abelian integrals; Picard variety; cohomology of sheaves; variation of cohomology; determinantal varieties; theta divisor Kempf, George, Abelian integrals, Monografías del Instituto de Matemáticas [Monographs of the Institute of Mathematics] 13, vii+225 pp., (1983), Universidad Nacional Autónoma de México, México Algebraic functions and function fields in algebraic geometry, Jacobians, Prym varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Picard schemes, higher Jacobians, Algebraic theory of abelian varieties, Theta functions and abelian varieties Abelian integrals
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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves over finite field; maximal curve; Hermitian curve Cossidente, A.; Korchmáros, G.; Torres, F., Curves of large genus covered by the Hermitian curve, Comm. Algebra, 28, 4707-4728, (2000) Curves over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry Curves of large genus covered by the Hermitian curve
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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 \(x^n+y^m+1=0\) rational points; algebraic curves and surfaces; projective varieties; Gröbner bases N. Broberg, ''A note on a paper by R. Heath-Brown: 'The density of rational points on curves and surfaces','' J. reine angew. Math., 571, 159--178 (2004). Varieties over global fields, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Counting solutions of Diophantine equations, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) A note on a paper by R. Heath-Brown: ``The density of rational points on curves and 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 \(x^n+y^m+1=0\) normal rational curve; arcs in projective space; M.D.S. codes; hypersurface Bruen, A. A.; Thas, J. A.; Blokhuis, A.: M.D.S. codes and arcs in projective space, I. C. R. Math. rep. Acad. sci. Canada 10, 225-230 (1988) Combinatorial structures in finite projective spaces, Algebraic functions and function fields in algebraic geometry, Combinatorial codes M.D.S. codes and arcs in projective space. I,II
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) anabelian geometry; section conjecture; hyperbolic curve; pro-\(p\) fundamental groups Hoshi Y., Existence of nongeometric pro-p Galois sections of hyperbolic curves, Publ. Res. Inst. Math. Sci. 46 (2010), 829-848. Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Existence of nongeometric pro-\(p\) Galois sections of hyperbolic 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 \(x^n+y^m+1=0\) mass formula; abelian varieties over finite fields Varieties over finite and local fields, Arithmetic ground fields for abelian varieties, Arithmetic theory of algebraic function fields On counting certain abelian varieties 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 \(x^n+y^m+1=0\) curve; function field; finite field; genus; rational point; Hasse-Weil bound Anbar, N; Stichtenoth, H, Curves of every genus with a prescribed number of rational points, Bull. Braz. Math. Soc. (N.S.), 44, 173-193, (2013) Curves over finite and local fields, Rational points, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Curves of every genus with a prescribed number of rational points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois extension; Galois group; \(G\)-covering; \(\mathbb{Q}_ p\)-rational points; inverse Galois problem Deschamps, B.: Existence de points p-adiques pour tout p sur un espace de Hurwitz. Proceedings AMS-NSF Summer Conference, 186, Cont. Math. series, Recent Developments in the Inverse Galois Problem, 111--171 (1995) Rational points, Inverse Galois theory, Coverings of curves, fundamental group, Arithmetic theory of algebraic function fields Existence of \(p\)-adic points for all \(p\) over a Hurwitz space
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) plane curves with many points; finite fields; cyclotomic fields; irreducible polynomials; height; many integral solutions; many rational zeros Rodríguez Villegas, F; Voloch, JF; Zagier, D, Constructions of plane curves with many points, Acta Arith., 99, 85-96, (2001) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Heights Constructions of plane curves with many 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 \(x^n+y^m+1=0\) rational points; bielliptic curve; elliptic Chabauty method; Weierstrass preparation theorem; genus 4 curve Higher degree equations; Fermat's equation, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Counting solutions of Diophantine equations, Power series rings, Rational points Rational points and the elliptic Chabauty method.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curve; Weierstrass point; Selmer group; Mordell-Weil group Benedict H. Gross, Hanoi lectures on the arithmetic of hyperelliptic curves, Acta Math. Vietnam. 37 (2012), no. 4, 579 -- 588. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Hanoi lectures on the arithmetic of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hilbert's 10th problem; algebraic integers; local-global principle; solvability of diophantine equations B. Green, F. Pop, P. Roquette, On Rumely's local-global principle. \textit{Jahresber. Deutsch. Math.-Verein}. \textbf{97} (1995), 43-74. MR1341772 Zbl 0857.11033 Varieties over global fields, Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry On Rumely's local-global principle
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) compactification; Drinfeld modules Formal groups, \(p\)-divisible groups, Arithmetic theory of algebraic function fields, Structure of families (Picard-Lefschetz, monodromy, etc.) Compactification of the scheme of Drinfeld modules.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Jacobian Kuribayashi curves; sextactic points Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus On the Jacobian of Kuribayashi 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 \(x^n+y^m+1=0\) inverse Galois problem; \(\ell\)-adic representations; abelian analytic functions Modular correspondences, etc., Arithmetic aspects of modular and Shimura varieties, Arithmetic theory of algebraic function fields, Coverings of curves, fundamental group, General theory for finite permutation groups Moduli relations between \(\ell\)-adic representations and the regular inverse Galois problem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cyclotomic function field; Jacobian; Hasse-Witt invariant Cyclotomic function fields (class groups, Bernoulli objects, etc.), Arithmetic theory of algebraic function fields, Jacobians, Prym varieties On the ordinarity of the maximal real subfield of cyclotomic 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 \(x^n+y^m+1=0\) Diophantine equation, curves of genus 0; integer valued polynomials, polynomial parametrization Representation problems, Polynomial rings and ideals; rings of integer-valued polynomials, Higher degree equations; Fermat's equation, Algebraic functions and function fields in algebraic geometry Polynomial parametrization of the solutions of Diophantine equations of genus 0
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Nakai-Moishezon theorem; arithmetic surface; discreteness of algebraic points on an algebraic curve; hermitian line bundle; canonical height S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. (2) 136 (1992), no. 3, 569-587. Arithmetic varieties and schemes; Arakelov theory; heights, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Arithmetic ground fields for curves Positive line bundles on arithmetic 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 \(x^n+y^m+1=0\) Guruswami, V.; Patthak, A.: Correlated algebraic-geometric codes: improved list decoding over bounded alphabets, Mathematics of computation 77, 447-473 (2008) Geometric methods (including applications of algebraic geometry) applied to coding theory, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry Correlated algebraic-geometric codes: improved list decoding over bounded alphabets
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Runge theorem; binary Diophantine equation; Puiseux series D. L. Hilliker, E. G. Straus, Determination of bounds for the solutions to those binary Diophantine equations that satisfy the hypotheses of Runge's theorem. Trans. Amer. Math. Soc. 280 (1983), no. 2, 637-657. Zbl0528.10011 Cubic and quartic Diophantine equations, Higher degree equations; Fermat's equation, Algebraic functions and function fields in algebraic geometry Determination of bounds for the solutions to those binary Diophantine equations that satisfy the hypotheses of Runge's theorem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic equations; integer solution; Chabauty-Coleman method; quadratic Chabauty method; Mordell-Weil sieve J. S. Balakrishnan, A. Besser, and J. S. Müller, Computing integral points on hyperelliptic curves using quadratic Chabauty, Math. Comp. 86 (2017), 1403--1434. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Computer solution of Diophantine equations, Arithmetic varieties and schemes; Arakelov theory; heights Computing integral points on hyperelliptic curves using quadratic Chabauty
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weierstrass semigroup; Weierstrass pair; Hermitian function field; sequences; nonlinear complexity Algebraic functions and function fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects) Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) The Rieman-Roch theorem. Algebraic functions and function fields in algebraic geometry The \textit{Riemann-Roch} theorem and the independence of the conditions of adjointness in the case of a curve, for which the tangents at the multiple points are distinct from one another.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Potts curves; stacks of hyperelliptic curves Families, moduli of curves (algebraic), Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves The stack of Potts curves and its fibre at a prime of wild ramification
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer group of the rational function fields Brauer groups of schemes, Galois cohomology, Arithmetic theory of algebraic function fields Groupe de Brauer des corps de fractions rationnelles à coefficients complexes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 subcover; refined Humbert invariant; Neron-Sevei group; quadratic form Coverings of curves, fundamental group, Jacobians, Prym varieties, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Elliptic subcovers of a curve of genus 2. I: The isogeny defect
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rank of elliptic curves; function field; multiplicative order Elliptic curves, Algebraic functions and function fields in algebraic geometry, Distribution of integers with specified multiplicative constraints, Class field theory Rank statistics for a family of elliptic curves over a function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) reciprocity law for surfaces over finite fields; group of degree 0 zero- cycles; rational equivalence; abelian geometric fundamental group; unramified class field theory; K-theory; Chow groups Jean-Louis Colliot-Thélène & Wayne Raskind, ``On the reciprocity law for surfaces over finite fields'', J. Fac. Sci. Univ. Tokyo Sect. IA Math.33 (1986) no. 2, p. 283-294 Finite ground fields in algebraic geometry, Coverings in algebraic geometry, Algebraic cycles, Parametrization (Chow and Hilbert schemes), Homotopy theory and fundamental groups in algebraic geometry, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic theory of algebraic function fields On the reciprocity law for surfaces 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 \(x^n+y^m+1=0\) affine curve; complete intersection point; geometrically unibranch singular point; rationality; rank of Pic; units; conductor; Mayer- Vietoris sequence E. D. Davis and P. Maroscia, Affine curves on which every point is a set-theoretic complete intersection, preprint. Algebraic functions and function fields in algebraic geometry, Complete intersections, Rational and unirational varieties, Singularities of curves, local rings, Picard groups Affine curves on which every point is a set-theoretic complete intersection
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Bogomolov conjecture; curves of higher genus; function fields; metric graphs Faber, X. W. C., The geometric Bogomolov conjecture for curves of small genus, Experiment. Math., 1058-6458, 18, 3, 347\textendash 367 pp., (2009) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic varieties and schemes; Arakelov theory; heights, Heights The geometric Bogomolov conjecture for curves of small genus
| 0 |
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