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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 \(x^n+y^m+1=0\) cyclic group automorphisms; Neron-Severi group; Jacobian; ring of endomorphisms Picard groups, Jacobians, Prym varieties, Relationships between algebraic curves and integrable systems, Special algebraic curves and curves of low genus On the Neron-Severi group of Jacobians of curves with automorphisms
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Artin conductor; efficient conductor; curves over local fields; sheaf of differential modules Arithmetic ground fields for curves, Local ground fields in algebraic geometry, \(p\)-adic cohomology, crystalline cohomology Inequality for conductor and differentials of a curve over a local field
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hyperelliptic curves; p-ranks, wild ramification, automorphisms of curves DOI: 10.1142/S1793042109002468 Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Automorphisms of curves The 2-ranks of hyperelliptic curves with extra 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 \(x^n+y^m+1=0\) vertex operator; parabolic bundle; Verlinde formula; Clebsch-Gordan condition; two dimensional conformal field theory; affine Lie algebra; conformal vacua; highest weight; moduli space of curves Franco, D.: An infinitesimal Torelli for conformal vacua. Comm. Algebra 31, 3795--3810 (2003) Vertex operators; vertex operator algebras and related structures, Vector bundles on curves and their moduli, Relationships between algebraic curves and integrable systems, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics An infinitesimal Torelli for conformal vacua
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 of curves; positive characteristic; quotients of the fundamental group; Abhyankar's conjecture; formal/rigid-analytic patching -, Fundamental groups of curves in characteristic \(p\), in Proceedings of the International Congress of Mathematicians, 1, 2 (Zürich, 1994), Birkhäuser, 1995, pp. 656-666. Coverings of curves, fundamental group, Homotopy theory and fundamental groups in algebraic geometry, Inverse Galois theory, Finite ground fields in algebraic geometry, Local ground fields in algebraic geometry Fundamental groups of curves in characteristic \(p\)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois representation; anabelian geometry; braid group; pro-\(l\) fundamental groups; groups of graded automorphisms; graded Lie algebras DOI: 10.1090/S0002-9947-98-02038-8 Coverings in algebraic geometry, Braid groups; Artin groups, Separable extensions, Galois theory, Fundamental groups and their automorphisms (group-theoretic aspects) Galois rigidity of pro-\(l\) pure braid groups of algebraic curves
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curves; finite Galois extension of degree n; Galois group; set of K-linear maps Galois theory, Arithmetic ground fields for curves, Elliptic curves over global fields, Elliptic curves An application of Mordell's conjecture to a characterization of Galois groups. I: Quadratic 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 \(x^n+y^m+1=0\) representation of finitely generated group; rational representations of pro-affine algebraic group; tangent spaces of the representation varieties; twist operation; orbits 6. Lubotzky, Alexander and Magid, Andy R. Varieties of representations of finitely generated groups \textit{Mem. Amer. Math. Soc.}58 (1985) 117 Math Reviews MR818915 (87c:20021) Classical groups (algebro-geometric aspects), Representation theory for linear algebraic groups, Ordinary representations and characters, Homological methods in group theory Varieties of representations of finitely generated 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 \(x^n+y^m+1=0\) Namba's conjecture; hypergeometric series over finite fields; elliptic curves; trace of the Frobenius map Koike, M., Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields, Hiroshima Math. J., 25, 1, 43-52, (1995) Curves over finite and local fields, Other character sums and Gauss sums, Classical hypergeometric functions, \({}_2F_1\), Special functions in characteristic \(p\) (gamma functions, etc.), Finite ground fields in algebraic geometry Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine group over the integers; Klein program; complete orbit invariant; Turing-computable invariant; \(\mathsf{GL}(n,\mathbb{Z})\)-orbit; (Farey)regular simplex; regular complex; desingularization; strong Oda conjecture; Hirzebruch-Jung continued fraction algorithm; rational polyhedron; conic; conjugate diameters; Apollonius of Perga; Pappus of Alexandria; quadratic form; Clifford-Hasse-Witt invariant; Hasse-Minkowski theorem; Markov unrecognizability theorem Actions of groups on commutative rings; invariant theory, Quadratic and bilinear Diophantine equations, General binary quadratic forms, Quadratic forms (reduction theory, extreme forms, etc.), Rational points, Plane and space curves, Geometric invariant theory, Toric varieties, Newton polyhedra, Okounkov bodies, Group actions on affine varieties, Other matrix groups over rings Complete and computable orbit invariants in the geometry of the affine group over the integers
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fixed point varieties on affine flag manifolds; simply connected semisimple algebraic group; variety of Borel subalgebras; Iwahori subalgebras; projective algebraic varieties; nilpotent orbits Chen, Z.: Truncated affine grassmannians and truncated affine Springer fibers for \({\mathrm GL}_{3}\). arXiv:1401.1930 Lie algebras of Lie groups, Linear algebraic groups over the reals, the complexes, the quaternions, Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations Fixed point varieties on affine flag manifolds
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic of rational points; varieties over function fields; cardinaltiy of the set of fibrations; uniform boundedness of rational points; distribution of rational points Enumerative problems (combinatorial problems) in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Rational points Remarks about uniform boundedness of rational points 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 \(x^n+y^m+1=0\) Brauer group; function field of the projective line Mestre, J.F. 1994.Annulation, par changement de variable, d'éléments de Br2(k(x)) ayant quatre pôles, SÉrie I Vol. 319, 529--532. Paris: C. R. Acad. Sci. Brauer groups of schemes, Arithmetic theory of algebraic function fields, Galois cohomology, Algebraic functions and function fields in algebraic geometry Base change killing of elements of \(\text{Br}_ 2 (k(x))\) with four poles
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) symmetric function; \(k\)-Schur function; Young tableaux; \(k\)-core; Coxeter group; Littlewood-Richardson coefficient; affine Grassmannian Berg, C.; Saliola, F.; Serrano, L., Combinatorial expansions for families of non-commutative \textit{k}-Schur functions Symmetric functions and generalizations, Grassmannians, Schubert varieties, flag manifolds Combinatorial expansions for families of noncommutative \(k\)-Schur 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 \(x^n+y^m+1=0\) upper bounds; divisors on algebraic curves over finite fields; minimum distance of geometric Goppa codes; gonality; modular curves; Gilbert- Varshamov bound; decoding algorithms Pellikaan R.: On the gonality of curves, abundant codes and decoding. In: Coding Theory and Algebraic Geometry, Luminy, 1991. Lecture Notes in Mathematics, vol. 1518, pp. 132--144. Springer, Berlin (1992). Geometric methods (including applications of algebraic geometry) applied to coding theory, Computational aspects of algebraic curves, Bounds on codes, Decoding On the gonality of curves, abundant codes and decoding
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Frobenius-linear endomorphism of De Rham cohomology group; Jacobian of the Fermat curve; crystalline Weil group; Frobenius matrices; Morita gamma function R. Coleman, On the Frobenius matrices of Fermat curves, \textit{p}-adic analysis, Lecture Notes in Math. 1454, Springer, Berlin (1990), 173-193. Local ground fields in algebraic geometry, de Rham cohomology and algebraic geometry, Arithmetic ground fields for curves On the Frobenius matrices of Fermat 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 \(x^n+y^m+1=0\) rationality problem, linear group quotients, affine extensions of semi-simple groups Bogomolov F., Böhning Chr., Graf von Bothmer H.-Chr., Rationality of quotients by linear actions of affine groups, Sci. China Math. (in press), DOI: 10.1007/s11425-010-4127-z Rationality questions in algebraic geometry, Rational and unirational varieties, Geometric invariant theory Rationality of quotients by linear actions of affine 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 \(x^n+y^m+1=0\) ordered fields; dense orbits property; automorphisms acting on spaces of orderings; behavior under field extensions; formally real field Gamboa J.\ M. and Recio T., Ordered fields with the dense orbits property, J. Pure Appl. Algebra 30 (1983), 237-246. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Algebraic field extensions, Transcendental field extensions, Ordered fields, Real algebraic and real-analytic geometry Ordered fields with the dense orbits 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 \(x^n+y^m+1=0\) Bogomolov conjecture over function fields; discrete embedding of curve; Néron-Tate height pairing; admissible pairing; Green function; semistable arithmetic surface A. Moriwaki, Bogomolov conjecture over function fields for stable curves with only irreducible fibers, Compos. Math. 105 (1997), 125-140. Algebraic functions and function fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Picard groups Bogomolov conjecture over function fields for stable curves with only irreducible fibers
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) distribution of ideal class groups of imaginary quadratic fields; distribution of class groups of hyperelliptic function fields; \(\ell\)-adic Tate module; equidistribution conjecture; Cohen-Lenstra principle Friedman, Eduardo; Washington, Lawrence C., On the distribution of divisor class groups of curves over a finite field.Théorie des nombres, Quebec, PQ, 1987, 227\textendash 239 pp., (1989), de Gruyter, Berlin Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry On the distribution of divisor class groups of curves over a finite field
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) computer algebra; polynomial factorization; reducible curves; function fields; divisors; algebraic extensions Duval D (1991) Absolute factorization of polynomials: a geometric approach. SIAM J Comput 20:1--21 Symbolic computation and algebraic computation, Polynomials in real and complex fields: factorization, Algebraic functions and function fields in algebraic geometry, Divisors, linear systems, invertible sheaves, Algebraic field extensions Absolute factorization of polynomials: A geometric approach
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Dirichlet twists of \(L\)-functions; Elliptic curves over number fields Fearnley, J.; Kisilevsky, H.; Kuwata, M., Vanishing and non-vanishing Dirichlet twists of \textit{L}-functions of elliptic curves, J. lond. math. soc. (2), 86, 2, 539-557, (2012) Elliptic curves over global fields, Rational points, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Global ground fields in algebraic geometry, \(K3\) surfaces and Enriques surfaces Vanishing and non-vanishing Dirichlet twists of \(L\)-functions 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 \(x^n+y^m+1=0\) elliptic curves with rank \(\geq 12\); curves over function fields Jean-François Mestre, Courbes elliptiques de rang \ge 12 sur \?(\?), C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 4, 171 -- 174 (French, with English summary). Elliptic curves over global fields, Elliptic curves, Arithmetic theory of algebraic function fields Elliptic curves with rank \(\geq 12\) over \(\mathbb Q(t)\)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mal'tsev completion of a discrete group; affine algebraic group; mapping class group; pro-unipotent completion; Torelli group; algebraic 1-cycle; Jacobian of an algebraic curve Hain, R., Completions of mapping class groups and the cycle \(C - C^-\), Contemp. math., 150, 75-105, (1993) General low-dimensional topology, Families, moduli of curves (algebraic), Fundamental groups and their automorphisms (group-theoretic aspects), Algebraic cycles, Affine algebraic groups, hyperalgebra constructions, Infinite-dimensional Lie (super)algebras, Infinite-dimensional Lie groups and their Lie algebras: general properties, Rational homotopy theory, Differential topological aspects of diffeomorphisms Completions of mapping class groups and the cycle \(C-C^ -\)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; plane cubics of genus one; exceptional points Nagell, T. Les points exceptionnels sur les cubiques planes du premier genre II, Nova Acta Reg. Soc. Sci. Ups., Ser. IV, vol 14, n:o 3, Uppsala 1947. Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Les points exceptionnels sur les cubiques planes du premier genre. 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 \(x^n+y^m+1=0\) cyclotomic function fields; arithmetic of Witt vectors; Artin-Schreier extensions; maximal abelian extension; ramification theory Cyclotomic function fields (class groups, Bernoulli objects, etc.), Cyclotomic extensions, Class field theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Analog of the Kronecker-Weber theorem in 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 \(x^n+y^m+1=0\) Stickelberger element; Galois module structure; Gras conjecture; Drinfeld modules; Herbrand criterion; crystalline cohomology; zeta-functions for function fields over finite fields; L-series; Teichmüller character; characteristic polynomial of the Frobenius; p-adic Tate-module; p-class groups; cyclotomic function fields; 1-unit root Goss, D., Sinnott, W.: Class-groups of function fields. Duke Math. J. 52(2), 507--516 (1985). http://www.ams.org/mathscinet-getitem?mr=792185 Arithmetic theory of algebraic function fields, \(p\)-adic cohomology, crystalline cohomology, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Iwasawa theory Class-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 \(x^n+y^m+1=0\) moduli space of hyperelliptic curves of arbitrary genus; moduli spaces for hyperelliptic curves with group action Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles, Group actions on varieties or schemes (quotients), Geometric invariant theory Automorphismengruppen und Moduln hyperelliptischer Kurven. (Automorphism groups and moduli 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 \(x^n+y^m+1=0\) differential Horace lemma; prescribed singularities; Picard group; cohomology groups of line bundles; plane curves; geometric genus Mignon, T., Courbes lisses sur les surfaces rationnelles génériques: Un lemme d'Horace différentiel, Ann. Inst. Fourier (Grenoble), 50, 6, 1709-1744, (2000) Rational and ruled surfaces, Plane and space curves, Configurations and arrangements of linear subspaces Smooth curves on generic rational surfaces: a differential Horace lemma
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 surface; Arakelov theory; discriminant; pairing on curves; intersection number of horizontal divisors; Green's functions; divisor group Harbater, D.: Arithmetic discriminants and horizontal intersections. Mathematische annalen 291, 705-724 (1991) Arithmetic varieties and schemes; Arakelov theory; heights, Divisors, linear systems, invertible sheaves, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Global ground fields in algebraic geometry, Local ground fields in algebraic geometry Arithmetic discriminants and horizontal intersections
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) towers of function fields; genus; number of places [HST]F. Hess, H. Stichtenoth and S. Tutdere, On invariants of towers of function fields over finite fields, J. Algebra Appl. 12 (2013), no. 4, #1250190. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On invariants of towers of function fields over finite fields
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer group; Prym variety; symmetric product of curves Algebraic cycles, Étale and other Grothendieck topologies and (co)homologies, Brauer groups of schemes, Algebraic moduli problems, moduli of vector bundles, Stacks and moduli problems Brauer groups of schemes associated to symmetric powers of smooth projective curves in arbitrary characteristics
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; hyperelliptic function fields; algebraic function field; holomorphic differentials; Hasse-Witt matrix; Cartier operator Kodama,T.,Washio,T.: Hasse-Witt matrices of hyperelliptic function fields. Sci. Bull. Fac. Educ. Nagasaki Univ.37, 9-15 (1986) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Hasse-Witt matrices of hyperelliptic function fields
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Heisenberg group; deformation theory; stack; hyperelliptic curves; moduli of vector bundles; heat equations; heat operators; Hitchin's connection DOI: 10.1090/S0894-0347-98-00252-5 Complex-analytic moduli problems, Algebraic moduli problems, moduli of vector bundles, Braid groups; Artin groups, Connections (general theory), Jacobians, Prym varieties On Hitchin's connection
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of points on Fermat curves over finite fields; intersection multiplicity; Bézout's theorem; Frobenius degeneration; intersection multiplicities Hefez, A.; Kakuta, N.: New bounds for Fermat curves over finite fields. Contemp. math. 123, 89-97 (1991) Arithmetic ground fields for curves, Finite ground fields in algebraic geometry, Enumerative problems (combinatorial problems) in algebraic geometry, Curves over finite and local fields New bounds for Fermat 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 \(x^n+y^m+1=0\) function fields; integral moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; ratios conjecture 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 integral moments and ratios of quadratic Dirichlet \(L\)-functions over monic irreducible polynomials in \(\mathbb{F}_q [T]\)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) valued function fields; genus change; algebraic function field; reduction of constants; rigid analytic geometry; non-discrete valuation; defect; ramification index Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Non-Archimedean valued fields, Arithmetic ground fields for surfaces or higher-dimensional varieties Genre des corps de fonctions valués après Deuring, Lamprecht et Mathieu. (Genus of valued function fields after Deuring, Lamprecht and Mathieu)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cohomology of function field of a curve; complete discretely valued field; function ring of curves; existence of noncrossed product division algebras; function field of \(p\)-adic curve E. Brussel and E. Tengan, \textit{Formal constructions in the Brauer group of the function field of a p-adic curve}, Transactions of the American Mathematical Society, to appear. Brauer groups of schemes, Curves over finite and local fields, Brauer groups (algebraic aspects), Finite-dimensional division rings Formal constructions in the Brauer group of the function field of a \(p\)-adic 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 \(x^n+y^m+1=0\) moduli spaces; projective varieties; classifying spaces; group cohomology; group homology; symmetry marked moduli spaces; group of automorphisms; Bagnera-de Franchis varieties; absolute Galois group Catanese, F., Topological methods in moduli theory, Bull. Math. Sci., 5, 3, 287-449, (2015) Surfaces of general type, Algebraic moduli problems, moduli of vector bundles, Families, moduli, classification: algebraic theory, Moduli, classification: analytic theory; relations with modular forms Topological methods in moduli 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 \(x^n+y^m+1=0\) number of mappings of algebraic curves; theorem of De Franchis; Mordell's conjecture over functions fields Algebraic functions and function fields in algebraic geometry, Rational and birational maps, Picard-type theorems and generalizations for several complex variables, Enumerative problems (combinatorial problems) in algebraic geometry, Global ground fields in algebraic geometry A higher dimensional analogue of Mordell's conjecture over function fields and related problems
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) graded Azumaya algebras; generalized Brauer group of algebras; group of grade-preserving automorphisms; central algebras Beattie, M.: Computing the Brauer group of graded Azumaya algebras from its subgroups. J. algebra 101, 339-349 (1986) Graded rings and modules (associative rings and algebras), Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Brauer groups of schemes Computing the Brauer group of graded Azumaya algebras from its subgroups
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves defined over fields of formal power series; reciprocity law; bad reduction Douai, Jean-Claude; Touibi, Chedly: Courbes définies sur LES corps de séries formelles et loi de réciprocité. Acta arith. 42, No. 1, 101-106 (1982/1983) Arithmetic theory of algebraic function fields, Galois cohomology, Galois cohomology, Coverings in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Global ground fields in algebraic geometry, Arithmetic ground fields for curves Curves defined over fields of formal power series, and a reciprocity law
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) surfaces of general type; quotients of products of curves; finite group actions Surfaces of general type, Group actions on varieties or schemes (quotients), Computational aspects of algebraic surfaces On semi-isogenous mixed 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 \(x^n+y^m+1=0\) elliptic curves over function fields; bad reduction; \(j\)-invariant; function field; Weierstrass equation Arithmetic theory of algebraic function fields, Elliptic curves, Elliptic curves over global fields, Elliptic curves over local fields Minimal number of points with bad reduction for elliptic curves over \(\mathbb{P}^1\)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli spaces of curves; curves with level structures; mapping class groups; Torelli group; homology and cohomology of groups; Johnson homomorphism; homological stability A. Putman, The Torelli group and congruence subgroups of the mapping class group, Moduli spaces of Riemann surfaces, IAS/Park City Math. Ser. 20, American Mathematical Society, Providence (2013), 169-196. Families, moduli of curves (analytic), Compact Riemann surfaces and uniformization, Classification theory of Riemann surfaces, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Topological properties of groups of homeomorphisms or diffeomorphisms, Groups acting on specific manifolds The Torelli group and congruence subgroups of the mapping class 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 \(x^n+y^m+1=0\) Artin braid group; Jacobian varieties; Hurwitz monodromy; moduli space of curves M. Fried, Combinatorial computation of moduli dimension of Nielsen classes of covers, Contemporary Mathematics 89 (1989), 61--79. Coverings of curves, fundamental group, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Separable extensions, Galois theory, Families, moduli of curves (algebraic), Coverings in algebraic geometry Combinatorial computation of moduli dimension of Nielsen classes of 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 \(x^n+y^m+1=0\) real genus; Klein surface; NEC group; group of automorphisms B. Mockiewicz, Real genus \(12\) , Rocky Mountain J. Math. 34 (2004), 1391-1398. Klein surfaces, Special algebraic curves and curves of low genus, Generators, relations, and presentations of groups, Fuchsian groups and their generalizations (group-theoretic aspects), Group actions on manifolds and cell complexes in low dimensions Real genus 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 \(x^n+y^m+1=0\) lifting; Oort Conjecture; curves over \(p\)-adic fields; inverse Galois theory; elementary \(p\)-groups; automorphism group M. Matignon, \(p\)-groupes abéliens de type \((p,...,p)\) et disques ouverts \(p\)-adiques, Prépublication 83 (1998), Laboratoire de Mathématiques pures de Bordeaux. Inverse Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Ramification problems in algebraic geometry, Formal methods and deformations in algebraic geometry, Local ground fields in algebraic geometry, Automorphisms of curves Abelian \(p\)-groups of type \((p,\dots,p)\) and \(p\)-adic open discs
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) class numbers; quadratic fields; class group; hyperelliptic curve; elliptic curves Mestre, J.-F., Corps quadratiques dont le 5-rang du groupe des classes est \(###\) 3, Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 315, 371-374, (1992) Class numbers, class groups, discriminants, Quadratic extensions, Elliptic curves over global fields, Elliptic curves Corps quadratiques dont le 5-rang du groupe des classes est \(\geqq\) 3. (Quadratic fields whose 5-rank of the class group is \(\geqq\) 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 \(x^n+y^m+1=0\) supergroups of automorphisms; supergeometry; supermanifold; elliptic supersymmetric curves; SUSY Levin, A. M., Supersymmetric elliptic curves, Funct. Anal. Appl., 21, 3, 243-244, (1987) Curves in algebraic geometry, Period matrices, variation of Hodge structure; degenerations, Applications of global differential geometry to the sciences, Families, moduli of curves (analytic) Supersymmetric 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 \(x^n+y^m+1=0\) global function fields; genus; geometry of numbers D. Kettlestrings and J.L. Thunder, The number of function fields with given genus, Contem. Math. 587 (2013), 141--149. Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry The number of function fields with given genus
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) variety of polydules; affine algebraic scheme; affine algebraic group scheme; Grunewald-O'Halloran condition Group actions on varieties or schemes (quotients), Representations of associative Artinian rings The properties of variety of polydules as affine algebraic scheme
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) enumeration of graphs; generating function; \(n\)-pointed genus 2 curves; stratification Bini, G.; Gaiffi, G.; Polito, M.: A formula for the Euler characteristic of M\‾2,n. Math. Z. 236, 491-523 (2001) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Enumeration in graph theory, Families, moduli of curves (algebraic) A formula for the Euler characteristic of \(\overline{\mathcal M}_{2,n}\).
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 \(x^n+y^m+1=0\) geometric heights; section of surjective morphisms; Mordell conjecture over function fields Esnault, Hélène; Viehweg, Eckart, Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields, Compos. Math., 0010-437X, 76, 1-2, 69\textendash 85 pp., (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for surfaces or higher-dimensional varieties Effective bounds for semipositive sheaves and for the height of points on curves over complex 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 \(x^n+y^m+1=0\) genus; hyperelliptic curves; strong boundedness conjecture; group of rational points; Jacobian varieties of hyperelliptic curves --, Sur certains sous-groupes de torsion de jacobiennes de courbes hyperelliptiques de genreg 1.Manuscr. Math. 92 (1) (1997), 47--63. Rational points, Jacobians, Prym varieties, Elliptic curves, Special algebraic curves and curves of low genus On certain torsion subgroups of Jacobians of hyperelliptic curves of genus \(g \geq 1\)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite fields; maximal curves; genus spectrum; classification problem; towers of curves Garcia A.: On curves with many rational points over finite fields. In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pp. 152--163. Springer, Berlin (2002). Curves over finite and local fields, Finite ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory On 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 \(x^n+y^m+1=0\) Jacobi theta function; holomorphic maps of curves; Laurent coefficients; quasi-modular forms; Jacobi forms M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, in \textit{The moduli space of curves (Texel Island, 1994)}, 165--172, Progr. Math., 129, Birkhäuser Boston, Boston, MA, 1995.Zbl 0892.11015 MR 1363056 Holomorphic modular forms of integral weight, Theta functions and abelian varieties, Theta functions and curves; Schottky problem, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Other groups and their modular and automorphic forms (several variables) A generalized Jacobi theta function and quasimodular 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 \(x^n+y^m+1=0\) cohomology of groups; unramified Brauer group; twisted multiplicative fields of invariants Jean Barge, Cohomologie des groupes et corps d'invariants multiplicatifs tordus, Comment. Math. Helv. 72 (1997), no. 1, 1 -- 15 (French, with English summary). Galois cohomology, Brauer groups of schemes Cohomology of groups and twisted multiplicative fields of invariants
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational function semifields of tropical curves; chip firing moves on tropical curves Foundations of tropical geometry and relations with algebra, Geometric aspects of tropical varieties, Max-plus and related algebras, Semifields Rational function semifields of tropical curves are finitely generated over the tropical semifield
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) weight distributions of families of codes; families of elliptic curves over finite fields; numbers of rational points on the curves Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Curves over finite and local fields Codes 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 \(x^n+y^m+1=0\) logarithmic height function; Fermat Last Theorem; finiteness conjectures in Diophantine geometry; degenerate set of integral points; analogy between the theory of Diophantine approximation in number theory and value distribution theory; Nevanlinna theory; local height function; abc- conjecture; size of integral points on elliptic curves P. Vojta, Diophantine Approximations and Value Distribution Theory, Lecture Notes in Math. 1239, Springer, Berlin, 1987. Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Research exposition (monographs, survey articles) pertaining to number theory, Value distribution theory in higher dimensions, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Arithmetic algebraic geometry (Diophantine geometry), Rational points, Arithmetic ground fields for curves, Global ground fields in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties Diophantine approximations and value distribution 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 \(x^n+y^m+1=0\) elliptic curves over global fields; arithmetic surfaces; zeta function; zeta integral; two-dimensional adelic spaces; harmonic analysis; Hasse zeta functions; analytic duality; boundary term; meromorphic continuation and functional equation; mean-periodic functions; Laplace; Carleman transform; generalized Riemann hypothesis; Birch and Swinnerton; Dyer conjecture; automorphic representations Fesenko, I.: Adelic approach to the zeta function of arithmetic schemes in dimension two. Moscow Math. J. \textbf{8}(2), 273-317 (2008) (http://www.maths.nottingham.ac.uk/personal/ibf/ada.pdf) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Generalized class field theory (\(K\)-theoretic aspects) Adelic approach to the zeta function of arithmetic schemes in dimension 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 on hyperelliptic curves; automorphism group; number of rational points Rational points, Elliptic curves, Birational automorphisms, Cremona group and generalizations Algebraic curves over \(\mathbb{Q}\) with many rational points and minimal automorphism 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 \(x^n+y^m+1=0\) AG codes; towers of function fields; generalized Hamming weights; order bounds; Arf semigroups; inductive semigroups Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Calculation of integer sequences, Commutative semigroups On the second Feng-Rao distance of algebraic geometry codes related to Arf semigroups
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) multiplicative structure; skew fields over number fields; Hasse; norm principle; algebraic group; group of rational points; quadratic forms; Skolem-Noether theorem; algebra of quaternions; class field theory; direct subgroup; Spin(f); SL(1,D); trace Platonov V P and Rapinchuk A S, Proceedings of Steklov Institute of Math. 1985, Issue 3 Quaternion and other division algebras: arithmetic, zeta functions, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Linear algebraic groups over global fields and their integers, Class field theory, Algebras and orders, and their zeta functions, Rational points The multiplicative structure of division rings over number fields and the Hasse norm 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 \(x^n+y^m+1=0\) hypermaps; Belyi function; automorphism group of a Riemann surface; canonical curve; fixed points Streit, Manfred, Homology, Belyĭ\ functions and canonical curves, Manuscripta Math., 90, 4, 489-509, (1996) Riemann surfaces; Weierstrass points; gap sequences, Birational automorphisms, Cremona group and generalizations, Differentials on Riemann surfaces, Coverings of curves, fundamental group Homology, Belyĭfunctions and canonical 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 \(x^n+y^m+1=0\) computational number theory; elliptic curve method; probabilistic algorithm; factorization method; multiplicative groups of elliptic curves over finite fields; running time; comparison Lenstra, H. W., Factoring integers with elliptic curves, \textit{Annals of Mathematics}, 126, 3, 649-673, (1987) Primes, Software, source code, etc. for problems pertaining to number theory, Elliptic curves, Finite ground fields in algebraic geometry, Analysis of algorithms and problem complexity Factoring integers with 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 \(x^n+y^m+1=0\) cycle class map; Chow group; decomposable cycles; indecomposable cycles; product of three elliptic curves Gordon, B.B., Lewis, J.D.: Indecomposable higher Chow cycles. In: The Arithmetic and Geometry of Algebraic Cycles (Banff, AB, 1998), vol. 548, pp. 193-224. Nato Science Series C: - Mathematical and Physical Sciences, vol. 548. Kluwer Academic Publication, Dordrecht (2000) Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic cycles, Parametrization (Chow and Hilbert schemes), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Indecomposable higher Chow cycles
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) regular \({\mathbb{C}}^*\)-actions; normal forms of curves; Euler characteristic; characterization of the affine plane M. Zaidenberg, Rational actions of the group \(\mathbf{C}^{*}\) on \(\mathbf{C}^{2}\), their quasi-invariants, and algebraic curves in \(\mathbf{C}^{2}\) with Euler characteristic 1, Soviet Math. Dokl. 31 (1985), 57-60. Group actions on varieties or schemes (quotients), Families, moduli, classification: algebraic theory, Rational and birational maps, Complex Lie groups, group actions on complex spaces Rational actions of the group \({\mathbb{C}}^*\) on \({\mathbb{C}}^ 2\), their quasi-invariants, and algebraic curves in \({\mathbb{C}}^ 2\) with Euler characteristic 1
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; algebraic function fields; positive characteristic; automorphism groups Automorphisms of curves, Algebraic functions and function fields in algebraic geometry Curves with more than one inner Galois point
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer groups; division algebras; central simple algebras; symbol algebras; cyclic algebras; cubic curves; ramification divisors; rational function fields [Fo] T. Ford,Division algebras that ramify only along a singular plane cubic curve, New York Journal of Mathematics1 (1995), 178--183, http://nyjm.albany.edu:8000/j/v1/ford.html. Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Skew fields, division rings, Algebraic functions and function fields in algebraic geometry Division algebras that ramify only along a singular plane cubic 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 \(x^n+y^m+1=0\) automorphisms of Mumford curves; \(p\)-adic triangle groups; Hurwitz groups Rigid analytic geometry, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Structure of modular groups and generalizations; arithmetic groups, Automorphisms of curves, Primitive groups, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations \(p\)-adic Hurwitz 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 \(x^n+y^m+1=0\) constructions of \((t,s)\)-sequences; \((t,m,s)\)-nets; survey; algebraic curves over finite fields; rational points Harald Niederreiter and Chaoping Xing, Nets, (\?,\?)-sequences, and algebraic geometry, Random and quasi-random point sets, Lect. Notes Stat., vol. 138, Springer, New York, 1998, pp. 267 -- 302. Pseudo-random numbers; Monte Carlo methods, Curves over finite and local fields, Arithmetic ground fields for curves, Numerical quadrature and cubature formulas Nets, \((t,s)\)-sequences, and 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 \(x^n+y^m+1=0\) Hasse-Weil bound; number of points; extension fields; exponential sums; function fields over finite fields Varieties over finite and local fields, Exponential sums, Other character sums and Gauss sums, Arithmetic ground fields for curves A comparision of the number of rational places of certain function fields to the Hasse-Weil bounds
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 curve of rank 12; isogeny; canonical height; independent points; class group; Selmer groups; imaginary quadratic fields of 3-rank 6 Jordi Quer, Corps quadratiques de 3-rang 6 et courbes elliptiques de rang 12, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 6, 215 -- 218 (French, with English summary). Special algebraic curves and curves of low genus, Quadratic extensions, Iwasawa theory, Elliptic curves, Arithmetic ground fields for abelian varieties Corps quadratiques de 3-rang 6 et courbes elliptiques de rang 12. (Quadratic fields with 3-rank 6 and elliptic curves with rank 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 \(x^n+y^m+1=0\) algebraic curves; algebraic function fields; positive characteristic; automorphism groups Automorphisms of curves, Algebraic functions and function fields in algebraic geometry Large odd prime power order automorphism groups of algebraic curves in any 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 \(x^n+y^m+1=0\) order of the Tate-Shafarevich group; conductor; discriminant; modular elliptic curves; Birch-Swinnerton-Dyer conjecture Goldfeld, D; Szpiro, L, Bounds for the order of the Tate-Shafarevich group, Compositio Math., 97, 71-87, (1995) \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves Bounds for the order of the Tate-Shafarevich group
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hasse principle; approximation theorems for homogeneous spaces; abelianization of Galois cohomology; affine algebraic groups; non-Abelian hypercohomology; Brauer-Grothendieck group Morishita, M.: Hasse principle and approximation theorems for homogeneous spaces. Algebraic number theory and related topics, Kyoto 1996 998, 102-116 (1997) Galois cohomology of linear algebraic groups, Rational points, Cohomology theory for linear algebraic groups, Research exposition (monographs, survey articles) pertaining to number theory, Galois cohomology Hasse principle and approximation theorems for homogeneous 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 \(x^n+y^m+1=0\) Mumford curves; Artin-Schreier-Mumford curves; automorphisms of curves G. Cornelissen and F. Kato, Mumford curves with maximal automorphism group, Proceedings of the American Mathematical Society 132 (2004), 1937--1941. Automorphisms of curves, Local ground fields in algebraic geometry Mumford curves with maximal automorphism 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 \(x^n+y^m+1=0\) value sets; finite fields; polynomials; towers of function fields Polynomials over finite fields, Algebraic functions and function fields in algebraic geometry A link between minimal value set polynomials and tamely ramified towers of function fields over finite fields
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; integral points; elliptic curves; integral solutions A. Bremner, Some simple elliptic surfaces of genus zero , Manuscripta Math. 73 (1991), 5-37. Elliptic curves over global fields, Cubic and quartic Diophantine equations, Global ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Special surfaces, Rational points Some simple elliptic surfaces of genus zero
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) ideals; Lie algebras of vector fields; derivation Lie algebras; affine varieties Siebert, T., Lie algebras of derivations and affine algebraic geometry over fields of characteristic 0, \textit{Math. Ann.}, 305, 271-286, (1996) Lie algebras of vector fields and related (super) algebras, Derivations, actions of Lie algebras, Lie (super)algebras associated with other structures (associative, Jordan, etc.), Infinite-dimensional Lie (super)algebras, Varieties and morphisms Lie algebras of derivations and affine algebraic geometry over fields of characteristic \(0\)
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 \(x^n+y^m+1=0\) Brauer group; complement of an affine hypersurface; Picard group Brauer groups of schemes, Hypersurfaces and algebraic geometry On the Brauer group for the main open set in the affine space
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rank of elliptic curves; torsion group; modular surface; elliptic Elliptic curves over global fields, Global ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations The rank of elliptic curves with nontrivial torsion 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 \(x^n+y^m+1=0\) rational solutions of cubic Diophantine equations; complex multiplication; elliptic curves; group of endomorphisms; rational points Wajngurt, C.: Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to complex multiplication. J. number theory 23, 80-85 (1986) Special algebraic curves and curves of low genus, Complex multiplication and abelian varieties, Cubic and quartic Diophantine equations, Rational points, Algebraic functions and function fields in algebraic geometry, Elliptic curves Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to complex multiplication
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rationality questions; rational points; Hasse-Weil \(L\)-function of modular elliptic curves; local-global principles; Selmer's curve; smooth projective varieties; Tate-Shafarevich group; Tate-Shafarevich conjecture; Selmer groups of elliptic curves; class field theory; Kolyvagin test classes Mazur B.: On the passage from local to global in number theory. Bull. Amer. Math. Soc. (N.S.) 29(1), 14--50 (1993) Global ground fields in algebraic geometry, Local ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Rational points, Arithmetic ground fields for surfaces or higher-dimensional varieties, Arithmetic ground fields for abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) On the passage from local to global in number 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 \(x^n+y^m+1=0\) Bilinear complexity; finite fields; algebraic function fields; algebraic curves Ballet, Stéphane; Chaumine, Jean, On the bounds of the bilinear complexity of multiplication in some finite fields, Appl. Algebra Engrg. Comm. Comput., 0938-1279, 15, 3-4, 205-211, (2004) Curves over finite and local fields, Arithmetic ground fields for curves, Arithmetic theory of algebraic function fields, Number-theoretic algorithms; complexity, Finite ground fields in algebraic geometry, Analysis of algorithms and problem complexity On the bounds of the bilinear complexity of multiplication in some 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 \(x^n+y^m+1=0\) algebraic curves; function field; automorphism group Danisman, Y.; Özdemir, M., On subfields of GK and generalized GK function fields, \textit{J. Korean Math. Soc.}, 52, 2, 225-237, (2015) Algebraic functions and function fields in algebraic geometry, Automorphisms of curves On subfields of GK and generalized GK 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 \(x^n+y^m+1=0\) group of k-rational points; affine algebraic group; topological irreducibility; unitary representations; algebraic irreducibility Representations of Lie and linear algebraic groups over local fields, Analysis on \(p\)-adic Lie groups, Affine algebraic groups, hyperalgebra constructions An irreducible smooth non-admissible representation
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 arithmetic ground fields; fundamental groups; categories; localization of categories; graph theory; profinite groups; free nonabelian groups Mochizuki S., Semi-graphs of anabelioids, Publ. Res. Inst. Math. Sci. 42 (2006), no. 1, 221-322. Coverings of curves, fundamental group, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Homotopy theory and fundamental groups in algebraic geometry, Arithmetic ground fields for curves, Localization of categories, calculus of fractions, Free nonabelian groups Semi-graphs of anabelioids
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) actions of an additive group on affine n-space Group actions on varieties or schemes (quotients) On actions of an additive group on \({\mathbb{A}}^ n\)
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 \(x^n+y^m+1=0\) postulation; Hilbert function; unions of curves Projective techniques in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series Postulations in projective spaces of unions of a fixed schemes and several high degree general 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 \(x^n+y^m+1=0\) Hasse-Witt matrix; hyperelliptic curves; hyperelliptic function fields; algebraic function field; class number; supersingular T. Washio and T. Kodama: A note on a supersingular function field. Sci. Bull. Fac. Ed. Nagasaki Univ., 37, 17-21 (1986). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry A note on a supersingular 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 \(x^n+y^m+1=0\) function field of homogeneous space; level of a field; equivariant cohomology; real abelian variety; Picard group Van Hamel, J., \textit{divisors on real algebraic varieties without real points}, Manuscripta Math., 98, 409-424, (1999) Real algebraic sets, Picard groups, Forms over real fields, Other nonalgebraically closed ground fields in algebraic geometry, Divisors, linear systems, invertible sheaves, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Divisors on real algebraic varieties without real 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 \(x^n+y^m+1=0\) genus-changing algebraic curves; finite number of rational points; characteristic \(p\); function field; non-conservative algebraic curve Jeong, S.: Rational points on algebraic curves that change genus. J. number theory 67, 170-181 (1998) Rational points, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Rational points on algebraic curves that change genus
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 fundamental group; hyperbolic affine curves; anabelian geometry; Grothendieck's anabelian conjecture T. Szamuely, Le théorème de Tamagawa I. In Courbes semi-stables et groupe fondamental en géométrie algébrique (Luminy, 1998), 185-201, Progr. Math. 187, Birkhäuser, Basel, 2000. Zbl0978.14014 MR1768101 Homotopy theory and fundamental groups in algebraic geometry, Coverings of curves, fundamental group, Global ground fields in algebraic geometry The Tamagawa theorem. 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 \(x^n+y^m+1=0\) analytic function germ; isolated singularities of complete intersections; monodromy group; contact invariant; fundamental group; Milnor fibers; Milnor numbers Dimca, A.: Monodromy of functions defined on isolated singularities of complete intersections. Compos. Math.54, 105-119 (1985) Local complex singularities, Germs of analytic sets, local parametrization, Homogeneous spaces and generalizations, Differentiable maps on manifolds, Theory of singularities and catastrophe theory Monodromy of functions defined on isolated singularities of complete intersections
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; function fields over finite fields; maximal curves Curves over finite and local fields, Arithmetic ground fields for curves, Jacobians, Prym varieties Optimal curves of low genus 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 \(x^n+y^m+1=0\) commuting pair of linear ordinary differential operators; vector bundle; classifications of the smooth elliptic curves; automorphism group; algebra of differential operators; indecomposable and decomposable bundles E. Previato and G. Wilson, \textit{Differential operators and rank }2 \textit{bundles over elliptic} \textit{curves}. Compositio Math. 81 (1992), no. 1, 107--119. General theory of ordinary differential operators, Vector bundles on curves and their moduli, Elliptic curves, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Differential operators and rank 2 bundles over 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 \(x^n+y^m+1=0\) Schottky group; determinant of Laplacian; Kronecker limit formula; Dedekind eta function; Liouville action; Schottky space; Teichmüller space; Green's function A. McIntyre and L.A. Takhtajan, \textit{Holomorphic factorization of determinants of laplacians on Riemann surfaces and a higher genus generalization of kronecker}'\textit{s first limit formula}, \textit{Analysis}\textbf{16} (2006) 1291 [math/0410294] [INSPIRE]. Determinants and determinant bundles, analytic torsion, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Families, moduli of curves (analytic), Compact Riemann surfaces and uniformization, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker's first limit formula
0