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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 \(x^n+y^m+1=0\) Siegel lemma; extrapolation; rank estimate; higher-dimensional Lehmer problem; power of the multiplicative group; lower bound; heights; successive minima for the height function Amoroso, F.; David, S., Le problème de Lehmer en dimension supérieure, J. Reine Angew. Math., 513, 145-179, (1999) Heights, Results involving abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights The higher-dimensional Lehmer problem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of curves; mapping class group; Mumford-Morita-Miller class; tautological algebra; symplectic group Morita S.: Generators for the tautological algebra of the moduli space of curves. Topology 42, 787--819 (2003) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Characteristic classes and numbers in differential topology, Families, moduli of curves (algebraic), Homology of classifying spaces and characteristic classes in algebraic topology, General low-dimensional topology Generators for the tautological algebra of the moduli space of curves.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) circular units; Jacobian of Fermat curves; Galois representations; pro-\(\ell\) braid groups; étale covering of projective 1-space; representation in outer automorphism group of profinite fundamental; group; absolute Galois group; completed group algebra; Tate module; Jacobi sums; Galois cohomology Y. Ihara: Profinite braid groups, Galois representations and complex multiplications. Ann. of Math., 123, 43-106 (1986). JSTOR: Galois theory, Jacobians, Prym varieties, Complex multiplication and abelian varieties, Special algebraic curves and curves of low genus, Coverings of curves, fundamental group, Global ground fields in algebraic geometry, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Galois cohomology Profinite braid groups, Galois representations and complex multiplications
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) discrete subgroups of Lie groups; affine group; Auslander conjecture; Milnor conjecture; flat affine manifold; Margulis invariant; quasi-translation; free group; Schottky group Smilga, I.: Proper affine actions on semisimple Lie algebras. arXiv:1406.5906 Discrete subgroups of Lie groups, Linear algebraic groups over finite fields, Linear algebraic groups over the reals, the complexes, the quaternions, Classical groups (algebro-geometric aspects), Other geometric groups, including crystallographic groups, Simple, semisimple, reductive (super)algebras, Automorphisms, derivations, other operators for Lie algebras and super algebras Proper affine actions on semisimple Lie algebras
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine schemes; singularities; Kähler differentials; spectra of integral group rings; finitely generated Abelian groups; singular points Group rings, Group rings of infinite groups and their modules (group-theoretic aspects), Singularities in algebraic geometry, Ideals in associative algebras, Modules of differentials On spectra of Abelian group rings.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curve cryptography; hyperelliptic curves over finite fields; algebraic function fields over finite fields Curves over finite and local fields, Jacobians, Prym varieties, Special algebraic curves and curves of low genus, Data encryption (aspects in computer science), Cryptography Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus \(2\) using base field operations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves over finite fields; sphere packings; survey; asymptotically good lattices; codes; algebraic number fields; function fields; open problems Michael A. Tsfasman, Global fields, codes and sphere packings, Astérisque 198-200 (1991), 373 -- 396 (1992). Journées Arithmétiques, 1989 (Luminy, 1989). Algebraic coding theory; cryptography (number-theoretic aspects), Arithmetic ground fields for curves, Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory, Lattice packing and covering (number-theoretic aspects) Global fields, codes and sphere packings
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Heegner points; \(L\)-functions; singular moduli of elliptic curves; discriminants of imaginary quadratic fields Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Arithmetic ground fields for curves Singular moduli at the Heegener points for general discriminants
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group of curve; product of projective curves; Betti numbers; diagonal quotient surface; desingularizations; Chern numbers; Enriques-Kodaira classification Kani E., Schanz W. (1997). Diagonal quotient surfaces. Manuscripta Math. 93(1):67--108 Homogeneous spaces and generalizations, Families, moduli, classification: algebraic theory, Singularities of surfaces or higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations, Curves in algebraic geometry Diagonal quotient 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 \(x^n+y^m+1=0\) semisimple, simply connected algebraic group; group scheme; maximal torus; character group; dominant weights; Coxeter number; G-module; group of rational points; injective hull; projective cover; affine Weyl group; fundamental dominant weights; Cartan invariants; composition factors; finite groups of Lie type Humphreys, J. E.: Generic Cartan invariants for Frobenius kernels and Chevalley groups. J. algebra 122, 345-352 (1989) Representation theory for linear algebraic groups, Group schemes, Linear algebraic groups over finite fields, Linear algebraic groups over arbitrary fields Generic Cartan invariants for Frobenius kernels and Chevalley 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 \(x^n+y^m+1=0\) curves with many points; algebraic function fields Rational points, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry On fibre products of Kummer curves with many rational points over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) analytic description of algebraic endomorphisms; extensions of elliptic curves by tori; transcendence; numbers related to Weierstrass sigma function; complex multiplication; algebraic groups; theta function BERTRAND (D.) et LAURENT (M.) . - Propriétés de transcendance de nombres liés aux fonctions thêta , C. r. Acad. Sci. Paris, Ser. A, t. 292, 1981 , p. 747-749. MR 82k:10037 | Zbl 0472.10033 Transcendence (general theory), Elliptic curves, Complex multiplication and abelian varieties Propriétés de transcendance de nombres liés aux fonctions thêta
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quasi-\(p\)-groups; Sylow \(p\)-subgroup; Galois group of a connected étale covering; covering of the affine line Michel Raynaud, ``Revêtements de la droite affine en caractéristique \(p > 0\) et conjecture d'Abhyankar'', Invent. Math.116 (1994) no. 1-3, p. 425-462{
}{\copyright} Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310 Coverings of curves, fundamental group, Local ground fields in algebraic geometry, Finite ground fields in algebraic geometry Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Alexander polynomial; fundamental group; analytic family of curves Oka, M.: Tangential Alexander polynomials and non-reduced degeneration, Singularities in geometry and topology, pp. 669-704. World Scientific Publishing, Hackensack (2007) Coverings of curves, fundamental group, Singularities of curves, local rings Tangential Alexander polynomials and non-reduced degeneration
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) group of birational automorphisms; minimal smooth rational; surfaces; Del Pezzo surface V.A. ISKOVSKIH . - Generators and relations in the group of birational automorphisms of two classes of rational surfaces , Trudy Mat. Inst. Steklov, 1984 , v. 165, 67-78. (= Proc. Steklov Inst. Math., 1985 , v. 165, 73-84). Zbl 0589.14012 Rational and birational maps, Special surfaces, Rational and unirational varieties Generators and relations in groups of birational automorphisms of two classes of rational surfaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves over positive characteristic; plane curve singularities; zeta functions; motivic zeta function; Poincaré series; local ring; semigroup of curve singularities Moyano-Fernández, J.J.; Zúñiga-Galindo, W.A., Motivic zeta functions for curve singularities, Nagoya Math. J., 198, 47-75, (2010) Singularities of curves, local rings, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), Zeta functions and \(L\)-functions Motivic zeta functions for curve singularities
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) central points; model class of fields; valuation; function field Bröcker, L.; Schülting, H. W.: Valuation theory from the geometrical point of view. J. reine angew. Math. 365, 12-32 (1986) Model theory of fields, Valued fields, Algebraic functions and function fields in algebraic geometry, Model-theoretic algebra Valuations of function fields from the geometrical point of view
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) subextremal curves; biliaison; spectrum of a curve; Rao function for curves Nollet S.: Subextremal curves. Manuscr. Math. 94(3), 303--317 (1997) Plane and space curves, Classical real and complex (co)homology in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Linkage Subextremal 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 \(x^n+y^m+1=0\) representations of central extension; conformal field theory; stable curves; gauge symmetries; integrable representations of Lie algebras; sheaf of twisted first order differential operators; monodromy; mapping class group Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Families, moduli of curves (algebraic) Moduli of stable curves, conformal field theory and affine Lie algebras
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli of curves; surfaces over number fields Arithmetic ground fields for surfaces or higher-dimensional varieties, Families, moduli of curves (algebraic), Coverings of curves, fundamental group Covers of moduli 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 \(x^n+y^m+1=0\) Schur group; classes in the Brauer group; group ring; extensions of automorphisms; decomposition of central simple algebras; Schur index Mollin, R. A.: More on the Schur group of a commutative ring. Internat. J. Math. math. Sci. 8, 275-282 (1985) Group rings, Finite rings and finite-dimensional associative algebras, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), Automorphisms and endomorphisms, Brauer groups of schemes More on the Schur group of a commutative ring
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) monster group; modular polynomial; coefficients; \(j\)-invariants of supersingular elliptic curves Modular and automorphic functions, Fourier coefficients of automorphic forms, Algebraic functions and function fields in algebraic geometry On Ito's observation on coefficients of the modular polynomial
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) actions of groups; linear algebra; topological groups; endomorphisms; Grassmannians; echelon matrices; groups preserving a bilinear form; quaternion fields; algebraic combinatorics; Lie groups; Platonic solids; topics from the projective plane; orthogonal groups; unitary groups; symplectic groups; Young tableaux; algebraic geometry; algebraic curves; surfaces configurations; special varieties; graphes; projective line; conics; representation theory; McKay correspondance Ph. Caldero, J. Germoni, \textit{Histoires Hédonistes de Groupes et de Géométries [Hedonistic Histories of Groups and Geometries].} Vol. 2, Calvage et Mounet, Paris, 2015. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry, Affine analytic geometry, Projective analytic geometry, Geometry of classical groups, Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations), Euclidean analytic geometry, Analytic geometry with other transformation groups, General theory of linear incidence geometry and projective geometries, Representations of finite symmetric groups, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Curves in algebraic geometry, Singularities of curves, local rings Hedonistic histories of groups and geometries. Vol. 2
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Grothendieck ring of varieties; motivic measure; \(\ell\)-adic Galois representations; weight filtration; zeta function; non-isogenous elliptic curves Naumann N.: Algebraic independence in the Grothendieck ring of varieties. Trans. Am. Math. Soc. 359(4), 1653--1683 (2007) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Varieties and morphisms, Motivic cohomology; motivic homotopy theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Varieties over finite and local fields Algebraic independence in the Grothendieck ring of varieties
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) existence of isometry-dual flags of codes; two-point algebraic geometry codes; isometry-dual property; two-point codes over function fields Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry The isometry-dual property in flags of two-point algebraic geometry codes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) groups of automorphisms; error correcting BCH-codes; linearized polynomial; hyperelliptic curves; number of rational points; Jacobians; Reed-Muller codes [8] G. van der Geer & M. van der Vlugt, `` Reed-Muller codes and supersingular curves. I {'', \(Compositio Math.\)84 (1992), no. 3, p. 333-367. Numdam | &MR 11 | &Zbl 0804.} Arithmetic ground fields for curves, Curves over finite and local fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Rational points Reed-Muller codes and supersingular curves. 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 \(x^n+y^m+1=0\) automorphisms of affine space; tame automorphisms; simplicial complex; automorphism of Nagata Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Combinatorial aspects of simplicial complexes, Polynomial rings and ideals; rings of integer-valued polynomials Combinatorics of the tame 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 \(x^n+y^m+1=0\) Richelot isogenies; superspecial abelian surfaces; reduced group of automorphisms; genus-2 isogeny cryptography Isogeny, Applications to coding theory and cryptography of arithmetic geometry, Automorphisms of curves, Jacobians, Prym varieties, Cryptography Counting Richelot isogenies between superspecial abelian surfaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; Riemann surfaces; automorphisms; field of moduli Compact Riemann surfaces and uniformization, Kleinian groups (aspects of compact Riemann surfaces and uniformization), Automorphisms of curves Orbifolds with signature \((0;k,k^{n-1},k^{n},k^{n})\)
| 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 \(x^n+y^m+1=0\) inverse problem of Galois theory; Fischer-Griess monster as Galois group over \({\mathbb{Q}}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_ 2({\mathbb{R}})\); congruence subgroup; modular curve; Puiseux-series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps; lectures Galois theory, Simple groups: sporadic groups, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Simple groups: alternating groups and groups of Lie type, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Some finite groups which appear as Gal L/K, where \(K\subseteq {\mathbb{Q}}(\mu _ n)\)
| 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 \(x^n+y^m+1=0\) fundamental group of the complement of a plane algebraic curve; nodal algebraic curves; computer algorithm S. Yu. Orevkov, ''The fundamental group of the complement of a plane algebraic curve,''Mat. Sb. [Math. USSR-Sb.],137 (179), No. 2, 260--270 (1988). Coverings in algebraic geometry, Singularities of curves, local rings, Software, source code, etc. for problems pertaining to algebraic geometry, Surfaces and higher-dimensional varieties The fundamental group of the complement of a plane algebraic 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 \(x^n+y^m+1=0\) simply connected affine algebraic group; extensions of irreducible modules; alcove transition Doty, S.R.; Sullivan, J.B.: On the geometry of extensions of irreducible modules for simple algebraic groups. Pacific J. Math. 130, 253-273 (1987) Affine algebraic groups, hyperalgebra constructions, Representation theory for linear algebraic groups On the geometry of extensions of irreducible modules for simple algebraic groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; Galois theory of function fields; Kummer theory; valuations; flag functions F.\ A. Bogomolov and Y. Tschinkel, Commuting elements of Galois groups of function fields, Motives, polylogarithms and Hodge theory. Part I (Irvine 1998), Int. Press Lect. Ser. 3, International Press, Somerville (2002), 75-120. Arithmetic theory of algebraic function fields, Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Configurations and arrangements of linear subspaces Commuting elements in Galois groups of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Swan conductor; wildness of ramification; Brauer group of a curve over a local field; Henselian discrete valuation fields Yamazaki T.: On Swan conductors for Brauer groups of curves over local fields. Proc. Amer. Math. Soc. 127, 1269-1274 (1999). Ramification problems in algebraic geometry, Brauer groups of schemes, Arithmetic ground fields for curves, Curves over finite and local fields, Local ground fields in algebraic geometry, Ramification and extension theory On Swan conductors for Brauer groups of curves over local fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cohomology of hyperbolic three-manifolds; automorphic representations; holomorphic Siegel modular forms; \(l\)-adic representations; elliptic curves over imaginary quadratic fields; Tate module; Ramanujan conjecture; \(L\)-function Taylor, Richard, \textit{l}-adic representations associated to modular forms over imaginary quadratic fields. II, Invent. Math., 116, 1-3, 619-643, (1994) Representation-theoretic methods; automorphic representations over local and global fields, Congruences for modular and \(p\)-adic modular forms, Cohomology of arithmetic groups, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Other groups and their modular and automorphic forms (several variables), Elliptic curves over global fields, Galois representations, Local ground fields in algebraic geometry \(l\)-adic representations associated to modular forms over imaginary quadratic fields. II
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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) inverse Galois problem; Galois extension of function field; Riemann- Hurwitz formula; genus; mock covers of curves DOI: 10.2307/2159335 Algebraic functions and function fields in algebraic geometry, Inverse Galois theory, Birational automorphisms, Cremona group and generalizations, Automorphisms of curves, Arithmetic theory of algebraic function fields, Curves in algebraic geometry The automorphism group of a function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global function fields; curves over finite fields; global square theorem; Picard groups; connected graphs; graph's diameter Curves over finite and local fields, Class groups and Picard groups of orders, Density theorems, Picard groups, Connectivity Even points on an algebraic 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 \(x^n+y^m+1=0\) extended space; homogeneous complex manifold; transitive group of analytic automorphisms; hypercircle; group of motions; classical symmetric domains; non-symmetric classical domains Homogeneous complex manifolds, Homogeneous spaces and generalizations Extended spaces of non-symmetric classical domains
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of primitive points; elliptic curves over number fields Voloch, J. F.: Primitive points on constant elliptic curves over function fields. Bol. soc. Bras. mat. 21, No. 1, 91-94 (1990) Elliptic curves, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Primitive points on constant elliptic curves over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; automorphisms of rational function field; Lüroth extensions; \(PSL({\mathbb{F}}_ q)\); holomorphic differentials; different; genus Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The genera of \(PSL({\mathbb{F}}_ q)\)-Lüroth coverings
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) action of reductive linear algebraic group on affine scheme; closed orbit; affine Cremona group; fixed points; étale slice theorem; linearizable actions; cancellation problem; linearization problem H. Bass,Algebraic group actions on affine spaces, in Contemporary Mathematics, Vol. 43, Am. Math. Soc., 1985, pp. 1--23. Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Birational automorphisms, Cremona group and generalizations Algebraic group actions on affine 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 \(x^n+y^m+1=0\) Jacobi quartic curves; Jacobi intersection curves; Tate pairing; Miller function; group law; geometric interpretation; birational equivalence Duquesne S, Fouotsa E (2013) Tate pairing computation on Jacobis elliptic curves. In: Proceedings of the 5th international conference on pairing based cryptography, pp. 254-269 (2012) Cryptography, Applications to coding theory and cryptography of arithmetic geometry, Analysis of algorithms Tate pairing computation on Jacobi's 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 \(x^n+y^m+1=0\) finite-dimensional complex matrix Lie supergroups; affine group superschemes; Hopf algebras of polynomial functions; real forms; Heisenberg supergroups; matrix realizations H. Boseck, Classical Lie supergroups, Math. Nachr. 148 (1990), 81--115. Infinite-dimensional Lie groups and their Lie algebras: general properties, Superalgebras, Supermanifolds and graded manifolds, Group schemes, Graded Lie (super)algebras, Loop groups and related constructions, group-theoretic treatment Classical Lie supergroups
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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 \(x^n+y^m+1=0\) computational complexity; algebraic geometry; irreducible polynomials; primitive polynomials; finite fields; polynomial factorization; distribution of primitive polynomials; construction of bases; algebraic number theory; computer science; coding theory; cryptography; factorization of bivariate polynomials; fast algorithms; discrete logarithm problem; fast exponentiation; polynomial multiplication; algebraic curves over finite fields; strengthening of the Weil-Serre bound; rational points; elliptic curves; distribution of primitive points; linear recurring sequences; automata; integer factorization; computational algebraic number theory; algebraic complexity theory; polynomials with integer coefficients 20.I. E. Shparlinski, \(Computational and algorithmic problems in finite fields\), Kluwer, Dordtrecht-Boston-London, 1992. Finite fields and commutative rings (number-theoretic aspects), Research exposition (monographs, survey articles) pertaining to number theory, Number-theoretic algorithms; complexity, Polynomials over finite fields, Arithmetic theory of polynomial rings over finite fields, Algebraic coding theory; cryptography (number-theoretic aspects), Analysis of algorithms and problem complexity, Geometric methods (including applications of algebraic geometry) applied to coding theory, Cryptography, Algebraic number theory computations, Rational points, Curves over finite and local fields Computational and algorithmic problems in 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 \(x^n+y^m+1=0\) cohomological dimension of fields; \(C_i\) property; Milnor K-theory; number fields; function fields Forms of degree higher than two, Hilbertian fields; Hilbert's irreducibility theorem, Field arithmetic, Other nonalgebraically closed ground fields in algebraic geometry, Higher symbols, Milnor \(K\)-theory, \(K\)-theory in number theory On a conjecture of Kato and Kuzumaki
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) complex multiplication; reciprocity laws for special values of Hilbert modular functions; arithmetic groups; Eisenstein series; maximal arithmetic groups; maximality of discrete groups of holomorphic automorphisms; adèle group; holomorphic modular forms Baily W L Jr, On the theory of Hilbert modular functions I, Arithmetic groups and Eisenstein series,J. Algebra 90 (1984) 567--605 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Complex multiplication and moduli of abelian varieties, Global ground fields in algebraic geometry On the theory of Hilbert modular functions. I: Arithmetic groups and Eisenstein series
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 group; action of an automorphism of order p; connected complete non-singular curves; tamely ramified Galois coverings; Witt vector ring Shōichi Nakajima, Action of an automorphism of order \? on cohomology groups of an algebraic curve, J. Pure Appl. Algebra 42 (1986), no. 1, 85 -- 94. Coverings of curves, fundamental group, Group actions on varieties or schemes (quotients), Classical real and complex (co)homology in algebraic geometry Action of an automorphism of order p on cohomology groups of an algebraic curve
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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) units in a ring; affine algebraic variety; group of units; class group; Galois cohomology; étale cohomology DOI: 10.1142/S0219498814500650 Divisibility and factorizations in commutative rings, Divisors, linear systems, invertible sheaves, Affine geometry The group of units on an affine variety
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) resolution of cusp singularities; Shintani decomposition; totally real cubic number fields; Hilbert modular variety; family of cubics; evaluation of zeta-function DOI: 10.1007/BF01359864 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Singularities of surfaces or higher-dimensional varieties, Special surfaces, \(3\)-folds, Totally real fields, Cubic and quartic extensions, Global ground fields in algebraic geometry On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite field; towers of algebraic function fields Arithmetic theory of algebraic function fields, Class field theory, Algebraic functions and function fields in algebraic geometry, Rational points A note on 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 \(x^n+y^m+1=0\) surfaces of general type; Albanese morphism; automorphisms; group actions; quotients; product-quotient surfaces; irregular surfaces; surfaces with \(p_g=q=2\) Surfaces of general type, Families, moduli, classification: algebraic theory, Automorphisms of surfaces and higher-dimensional varieties, Isogeny, Group actions on varieties or schemes (quotients) Quotients of the square of a curve by a mixed action, further quotients and Albanese morphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 quotients of group actions; equivariant cohomology; stratification; Morse function; Hodge numbers F.C. Kirwan, \textit{Cohomology of quotients in symplectic and algebraic geometry}, Princeton University Press, Princeton U.S.A. (1984). Group actions on varieties or schemes (quotients), Homology with local coefficients, equivariant cohomology, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Transcendental methods, Hodge theory (algebro-geometric aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Homogeneous spaces and generalizations Cohomology of quotients in symplectic 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 \(x^n+y^m+1=0\) deformations of Klein curve; group of automorphisms; deformations of Riemann surfaces; Torelli theorem; abelian differentials; Hodge decomposition; geodesics; quadratic differentials Algebraic functions and function fields in algebraic geometry, Differentials on Riemann surfaces, Transcendental methods, Hodge theory (algebro-geometric aspects), Fuchsian groups and their generalizations (group-theoretic aspects), Analytic theory of abelian varieties; abelian integrals and differentials, Families, moduli of curves (analytic), Complex Lie groups, group actions on complex spaces Deformations of Klein's curve and representations of its group of 168 automorphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Schottky group; non-archimedean valued fields; sheaves of normed; vector spaces; vector-bundle on the Mumford curve; semi-stable; vector bundle M. van der Put etM. Reversat, Fibrés vectoriels semi-stables sur une Courbe de Mumford. Math. Ann.273, 573--600 (1986). Local ground fields in algebraic geometry Fibrés vectoriels semi-stables sur une courbe de Mumford
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quadratic forms; function field of a quadric; Pfister forms; Pfister neighbor; Galois cohomology; unramified cohomology; Voevodsky's motivic cohomology; Chow group B. KAHN - R. SUJATHA, Motivic cohomology and unramified cohomology of quadrics. J. Eur. Math. Soc. (JEMS), 2 no. 2 (2000), pp. 145-177. Zbl1066.11015 MR1763303 Quadratic forms over general fields, Quadratic spaces; Clifford algebras, Galois cohomology, Étale and other Grothendieck topologies and (co)homologies, Motivic cohomology; motivic homotopy theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Motivic cohomology and unramified cohomology of quadrics
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Euler product; arithmetic surface; Jacobian zeta function; modular curve; survey; Dirichlet series; L-series of elliptic curves; conjecture of Birch and Swinnerton-Dyer; Hasse-Weil conjecture; analytic continuation; functional equation; Shimura-Taniyama conjecture; Serre's conjecture; modular representations Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Other Dirichlet series and zeta functions L-series of elliptic curves: Results, conjectures and consequences
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) general K3-surfaces in the 3-dimensional flag variety projective 2-space; group of automorphisms; orthochronous Lorentz group; Picard group J. Wehler, \(K\)3-surfaces with Picard number 2. Arch. Math. (Basel) 50(1), 73-82 (1988) Special surfaces, Quadratic extensions, Group actions on varieties or schemes (quotients), \(K3\) surfaces and Enriques surfaces, Automorphisms of surfaces and higher-dimensional varieties K3-surfaces with Picard number 2
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) local symbol; integral polynomials over quartic number fields; ramification; Polya field with class number one; product formula of local group homomorphisms; Brauer groups of global fields; decomposition group; Frobenius element; Stickelberger congruence; quadratic reciprocity law Zantema, H., ?Global restrictions on ramification in number fields?, to appear Other number fields, Galois cohomology, Ramification and extension theory, Cubic and quartic extensions, Brauer groups of schemes, Class numbers, class groups, discriminants, Polynomials (irreducibility, etc.), Galois cohomology, Power residues, reciprocity Global restrictions on ramification in number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves of genus two; Jacobians; canonical height; infinite descent; Mordell-Weil group; algorithm E.V. Flynn and N.P. Smart, Canonical heights on the Jacobians of curves of genus 2 and the infinite descent, Acta Arith., 79 (1997), 333-352. MR 98f:11066 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of curves; cohomology of the mapping class group; orientable surfaces; characteristic classes; Mumford-Morita-Miller classes Kawazumi, N., Morita, S.: The primary approximation to the cohomology of the moduli space of curves and cocycles for the Mumford-Morita-Miller classes. http://kyokan.ms.u-tokyo.ac.jp/users/preprint/pdf/2001-13.pdf (\textbf{Preprint}) Families, moduli of curves (algebraic), Characteristic classes and numbers in differential topology, (Co)homology theory in algebraic geometry The primary approximation to the cohomology of the moduli space of curves and cocycles for the stable characteristic classes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; vector fields; Lie algebras; affine \(n\)-space Lie algebras of vector fields and related (super) algebras, Jacobian problem Automorphisms of the Lie algebra of vector fields on affine \(n\)-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 \(x^n+y^m+1=0\) ruled function fields; Zariski problem; finitely generated extensions; automorphisms James K. Deveney, Automorphism groups of ruled function fields and a problem of Zariski, Proc. Amer. Math. Soc. 90 (1984), no. 2, 178 -- 180. Transcendental field extensions, Algebraic functions and function fields in algebraic geometry Automorphism groups of ruled function fields and a problem of Zariski
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Gromov-Witten invariants; group actions; Hamiltonian invariants; torus actions; geometric quotients; stable curves; symplectic geometry; number of rational curves Halic, M.: GW Invariants and Invariant Quotients. Comment. Math. Helv. 77, 145--191 (2002) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Families, moduli of curves (algebraic), Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Enumerative problems (combinatorial problems) in algebraic geometry GW invariants and invariant quotients
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 for solutions of diophantine equations; Runge theorem; finiteness of number of solutions; Brauer-Siegel theorem; Baker-Coates theory; linear forms in logarithms of algebraic numbers; \(p\)-adic case; representation of numbers by binary forms; Thue equation; rational approximations to algebraic numbers; effective strengthening of Liouville inequality; solution of Thue equation in \(S\)-integers; non-Archimedean metrics; polynomial equation; Mordell equation; Catalan equation; size of ideal class group; small regulator; effective variants of Hilbert on irreducibility of polynomials; Abelian points on algebraic curves Sprindžuk, Vladimir G., Classical Diophantine Equations, Lecture Notes in Mathematics 1559, xii+228 pp., (1993), Springer-Verlag, Berlin Diophantine equations, Diophantine approximation, transcendental number theory, Research exposition (monographs, survey articles) pertaining to number theory, Polynomials (irreducibility, etc.), Class numbers, class groups, discriminants, Arithmetic problems in algebraic geometry; Diophantine geometry Classical diophantine equations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) definition of an affine algebraic group; group inversion Affine algebraic groups, hyperalgebra constructions On definition of affine algebraic groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) inverse problem of Galois theory; Fischer-Griess monster as Galois group over \(\mathbb{Q}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_2(\mathbb{R})\); congruence subgroup; modular curve; Puiseux series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps J. Thompson , Some finite groups which appear as Gal (L/K) where K \subset Q(\mu n) , J. Alg. 89 (1984) 437-499. Galois theory, Simple groups: sporadic groups, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Simple groups: alternating groups and groups of Lie type, Unimodular groups, congruence subgroups (group-theoretic aspects), Finite automorphism groups of algebraic, geometric, or combinatorial structures, Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Some finite groups which appear as \(\mathrm{Gal } L/K\), where \(K\subseteq \mathbb{Q}(\mu_n)\)
| 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 \(x^n+y^m+1=0\) characteristic \(p\); good reduction; constructing unramified coverings of the affine line; modular curves; Galois groups of unramified coverings of the affine line; Klein curve; Macbeath curve; big automorphism groups; Jacobian varieties Coverings of curves, fundamental group, Inverse Galois theory, Finite ground fields in algebraic geometry, Jacobians, Prym varieties, Special algebraic curves and curves of low genus Construction techniques for Galois coverings of the affine line
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) mirror symmetry; mirror map; complete intersection Calabi-Yau spaces; Picard-Fuchs equations; instanton corrected Yukawa couplings; topological oneloop partition function; higher dimensional moduli spaces; closed formulas; prepotential; Kä|hler moduli fields; singular ambient space; nonsigular weighted projective spaces; three generation models; topology change; local solutions; topological invariants; Calabi-Yau manifold; rational superconformal field theories; elliptic curves; \(E_6\) gauge couplings; \(E_8\) gauge couplings; threshold corrections; Gromov-Witten invariants S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, \textit{Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces}, \textit{Nucl. Phys.}\textbf{B 433} (1995) 501 [hep-th/9406055] [INSPIRE]. Applications of deformations of analytic structures to the sciences, Calabi-Yau manifolds (algebro-geometric aspects), String and superstring theories; other extended objects (e.g., branes) in quantum field theory Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau 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 \(x^n+y^m+1=0\) action; group of \({\mathbb{C}}\)-algebra automorphisms; reflexive modules; almost split sequences; Auslander-Reiten quiver; McKay graph; desingularization graph; singularity Auslander M.: Rational singularities and almost split sequences. Trans. Am. Math. Soc. 293(2), 511--531 (1986) Representation theory for linear algebraic groups, Linear algebraic groups over the reals, the complexes, the quaternions, Singularities of surfaces or higher-dimensional varieties, Regular local rings, Representation theory of associative rings and algebras, Vector and tensor algebra, theory of invariants Rational singularities and almost split sequences
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) construction of Galois extensions; Galois group; rational curves; division points; elliptic curves; Chebotarev density theorem Asada, M.: Construction of certain non-solvable unramified Galois extensions over the total cyclotomic field. J. fac. Sci. univ. Tokyo sect. IA math. 32, 397-415 (1985) Galois theory, Cyclotomic extensions, Elliptic curves, Rational points Construction of certain non-solvable unramified Galois extensions over the total cyclotomic 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 \(x^n+y^m+1=0\) invariant field of automorphism group; rational function field; rationality problem Rational and unirational varieties, Group actions on varieties or schemes (quotients), Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Actions of groups on commutative rings; invariant theory Finite group actions on rational function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) tensor product of quaternion algebras; central simple algebras; orthogonal involution; Brauer-Severi variety; involution variety; function fields; generic isotropic splitting field; Brauer groups; Quillen \(K\)-theory D. Tao, ''A variety associated to an algebra with involution'',J. Algebra,168, 479--520 (1994). Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Rings with involution; Lie, Jordan and other nonassociative structures, Brauer groups of schemes, Computations of higher \(K\)-theory of rings, Homogeneous spaces and generalizations A variety associated to an algebra with involution
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; Mordell-Weil group; twist theory Yamagishi, H, On certain twisted families of elliptic curves of rank 8, Manuscr. Math., 95, 1-10, (1998) Elliptic curves over global fields, Elliptic curves On certain twisted families of elliptic curves of rank 8
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) isogeny graphs; \((\ell, \ell)\)-isogenies; principally polarised abelian varieties; Jacobians of hyperelliptic curves; lattices in symplectic spaces; orders in CM-fields Abelian varieties of dimension \(> 1\), Isogeny Isogeny graphs of ordinary abelian varieties
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) triangular transformations group; affine space; wreath product of translation groups Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Birational automorphisms, Cremona group and generalizations Automorphisms of Jonquiear's type groups 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 \(x^n+y^m+1=0\) isomorphism classes; hyperelliptic curves of genus 2; finite fields; hyperelliptic curve cryptography Choie Y., Yun D.: Isomorphism classes of hyperelliptic curves of genus \(2\) over \({\mathcal{F}}_{2}^{n}\). In: Proceedings of the ACISP 2002. LNCS, vol. 2384, pp. 190-202 (2002). Curves over finite and local fields, Elliptic curves over local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Cryptography Isomorphism classes of hyperelliptic curves of genus 2 over \(\mathbb{F}_q\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism of a Klein surface; period matrix; group of automorphisms Riera, J. London Math. Soc. 51 pp 442-- (1995) Riemann surfaces; Weierstrass points; gap sequences, Birational automorphisms, Cremona group and generalizations Automorphisms of abelian varieties associated with Klein 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 \(x^n+y^m+1=0\) action of linear group; prehomogeneous vector spaces; roots of b- function; castling transform Igusa, J.: On certain class of prehomogeneous vector spaces. J. pure appl. Algebra 47, 265-282 (1987) Homogeneous spaces and generalizations, Linear algebraic groups over arbitrary fields, Group actions on varieties or schemes (quotients) On a certain class of prehomogeneous vector 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 \(x^n+y^m+1=0\) hyperelliptic curves; automorphisms; field of moduli; field of definition Fuertes, Y.: Fields of moduli and definition of hyperelliptic curves of odd genus, Arch. math. (Basel) 95, 15-81 (2010) Automorphisms of curves, Special algebraic curves and curves of low genus, Arithmetic problems in algebraic geometry; Diophantine geometry Fields of moduli and definition of hyperelliptic curves of odd 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 \(x^n+y^m+1=0\) character variety; Hodge-Deligne polynomial; E-polynomial; parabolic Higgs bundles; doubly periodic instantons; representations of fundamental group; punctured curves Algebraic moduli problems, moduli of vector bundles, Transcendental methods, Hodge theory (algebro-geometric aspects), Geometric invariant theory Hodge polynomials of the \(\mathrm{SL}(2,\mathbb{C})\)-character variety of an elliptic curve with two marked 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 \(x^n+y^m+1=0\) rank of elliptic curves; function field; multiplicative order Elliptic curves, Algebraic functions and function fields in algebraic geometry, Distribution of integers with specified multiplicative constraints, Class field theory Rank statistics for a family of elliptic curves over a function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tate-Shafarevich group; local-global principle; patching; central simple algebras; Brauer group; arithmetic duality; function fields; higher-dimensional local fields Izquierdo, Diego Principe local-global pour les corps de fonctions sur des corps locaux supérieurs I \textit{J.~Number Theory}157 (2015) 250--270 Math Reviews MR3373241 Galois cohomology of linear algebraic groups, Galois cohomology, Other nonalgebraically closed ground fields in algebraic geometry, Galois cohomology Local-global principle for function fields over higher local fields. 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 \(x^n+y^m+1=0\) reciprocity law for surfaces over finite fields; group of degree 0 zero- cycles; rational equivalence; abelian geometric fundamental group; unramified class field theory; K-theory; Chow groups Jean-Louis Colliot-Thélène & Wayne Raskind, ``On the reciprocity law for surfaces over finite fields'', J. Fac. Sci. Univ. Tokyo Sect. IA Math.33 (1986) no. 2, p. 283-294 Finite ground fields in algebraic geometry, Coverings in algebraic geometry, Algebraic cycles, Parametrization (Chow and Hilbert schemes), Homotopy theory and fundamental groups in algebraic geometry, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic theory of algebraic function fields On the reciprocity law for surfaces over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine curves; global fields; Kodaira-Spencer class Gerd Faltings , Does there exist an arithmetic Kodaira-Spencer class? , Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), Contemp. Math. 241, American Mathematical Society, 1999, p. 141-146 Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Varieties over global fields, Arithmetic ground fields for curves Does there exist an arithmetic Kodaira-Spencer class?
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) p-adic L-function; Tate-module of an elliptic curve; Iwasawa-modules; CM- curves; two variable main conjecture Coates, J.; Schmidt, C.-G., Iwasawa theory for the symmetric square of an elliptic curve, Journal für die Reine und Angewandte Mathematik, 375/376, 104-156, (1987) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, Special algebraic curves and curves of low genus, Arithmetic ground fields for curves Iwasawa theory for the symmetric square of an elliptic 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 \(x^n+y^m+1=0\) dessins d'enfants; origami curves; Grothendieck-Teichmüller group; Veech group, cusps of origami curves Herrlich, F; Schmithüsen, G, Dessins d'enfants and origami curves, Handb. Teichmüller Theory, 2, 767-809, (2009) Compact Riemann surfaces and uniformization, Teichmüller theory for Riemann surfaces, Families, moduli of curves (analytic), Families, moduli of curves (algebraic), Elliptic curves Dessins d'enfants and origami curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine varieties; curves; projective; varieties; textbooks in algebraic geometry; local properties of varieties Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Foundations of algebraic geometry, Curves in algebraic geometry, Surfaces and higher-dimensional varieties, Projective and enumerative algebraic geometry Algebraic varieties
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; genus 2 curves; moduli space; elliptic fields; invariant theory Shaska T. (2004). Genus 2 fields with degree 3 elliptic subfields. Forum Math. 16(2):263--280 Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Special algebraic curves and curves of low genus, Arithmetic algebraic geometry (Diophantine geometry) Genus 2 fields with degree 3 elliptic subfields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) specialization of Galois extensions; function fields; Chebotarev property; Hilbert's irreducibility theorem; local and global fields Checcoli, S.; Dèbes, P.: Tchebotarev theorems for function fields. (2013) Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Hilbertian fields; Hilbert's irreducibility theorem, Field arithmetic, Arithmetic problems in algebraic geometry; Diophantine geometry Tchebotarev theorems for function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) public key cryptography; discrete logarithm; abelian varieties over finite fields; Jacobian varieties of hyperelliptic curves; Galois theory; Weil descent; Tate duality G. Frey, Applications of arithmetical geometry to cryptographic constructions, in Proceedings of the Fifth International Conference on Finite Fields and Applications (Springer, Berlin, 2001), pp. 128--161 Cryptography, Applications to coding theory and cryptography of arithmetic geometry Applications of arithmetical geometry to cryptographic constructions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic functions of one variable; algebraic function fields; arbitrary field of constants Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Fields of algebraic functions of one variable over an arbitrary field of constants
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) defect of the valued function fields; genus; ramification index Michel Matignon, Genre et genre résiduel des corps de fonctions valués, Manuscripta Math. 58 (1987), no. 1-2, 179 -- 214 (French, with English summary). Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Ramification problems in algebraic geometry, Valued fields Genre et genre residuel des corps de fonctions valués. (Genus and residual genus of valued function fields)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine Cremona group; automorphism of affine space; tame automorphism Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Birational automorphisms, Cremona group and generalizations Generating properties of biparabolic polynomial transformations of affine 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 \(x^n+y^m+1=0\) Galois representations; big monodromy; elliptic curves over function fields; Galois groups Galois representations, Elliptic curves over global fields, Structure of families (Picard-Lefschetz, monodromy, etc.) Galois groups arising from families with big orthogonal monodromy
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(l\)-adic Abel-Jacobi map; group of codimension-\(n\) cycles modulo rational equivalence; filtration; \(l\)-adic étale cohomology; cycle map; function field in one variable W. Raskind, ''Higher \(l\)-adic Abel-Jacobi mappings and filtrations on Chow groups,'' Duke Math. J., vol. 78, iss. 1, pp. 33-57, 1995. Algebraic cycles, Local ground fields in algebraic geometry, Parametrization (Chow and Hilbert schemes), Étale and other Grothendieck topologies and (co)homologies Higher \(l\)-adic Abel-Jacobi mappings and filtrations on Chow 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 \(x^n+y^m+1=0\) supercurve; Arf function; super-Fuchsian group; moduli space of rank 2 spinor bundles Supermanifolds and graded manifolds, Complex supergeometry, Supervarieties, Families, moduli of curves (analytic) Moduli spaces of real algebraic \(N=2\) supercurves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of smooth curves; rational points group of the Picard scheme; canonical divisor class DOI: 10.1007/BF01389421 Picard groups, Families, moduli of curves (algebraic), Rational points Conjecture de Franchetta forte. (Strong Franchetta conjecture)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) plane algebraic curves; characteristic variety; fundamental group of the complement to the curve A. Libgober, Characteristic varieties of algebraic curves, Applications of algebraic geometry to coding theory, physics and computation (Eilat, 2001) NATO Sci. Ser. II Math. Phys. Chem., vol. 36, Kluwer Acad. Publ., Dordrecht, 2001, pp. 215 -- 254. Plane and space curves, Homotopy theory and fundamental groups in algebraic geometry, Singularities of curves, local rings Characteristic varieties 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 \(x^n+y^m+1=0\) Brauer groups; Hasse principle; function fields of genus 1 Brauer groups of schemes, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus A method of computing the constant field obstruction to the Hasse principle for the Brauer groups of genus one 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 \(x^n+y^m+1=0\) automorphisms of algebraic groups; embedding of the affine line; principal bundles Group actions on varieties or schemes (quotients), Linear algebraic groups over the reals, the complexes, the quaternions, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms of surfaces and higher-dimensional varieties, Affine fibrations, Grassmannians, Schubert varieties, flag manifolds Uniqueness of embeddings of the affine line into algebraic groups
| 0 |
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