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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 \(x^n+y^m+1=0\) connected simply connected simple algebraic \(\mathbb{Q}\)-groups; smooth affine group schemes of finite type; special fibres; \(\mathbb{Q}\)-groups admitting \(\mathbb{Z}\)-models; Euler-Poincaré characteristic; mass formula; adjoint representations B.H. Gross, Groups over \(\(\mathbb {Z}\)\). Invent. Math. 124(1-3), 263-279 (1996) Linear algebraic groups over global fields and their integers, Group schemes Groups over \(\mathbb{Z}\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) normal basis; optimal normal bases; elliptic curves over finite fields; elliptic curve cryptosystems; codes; finite fields; finite field arithmetic; factoring of polynomials; discrete logarithm problem; irreducible polynomials; survey Menezes, A. J., Blake, I. F., Gao, X., Mullin, R. C., Vanstone, S. A., \& Yaghoobian, T. (1993). Applications of finite fields. Kluwer international series in engineering and computer science. ISBN: 0-7923-9282-5. Finite fields and commutative rings (number-theoretic aspects), Research exposition (monographs, survey articles) pertaining to number theory, Structure theory for finite fields and commutative rings (number-theoretic aspects), Algebraic coding theory; cryptography (number-theoretic aspects), Cryptography, Geometric methods (including applications of algebraic geometry) applied to coding theory, Elliptic curves, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Polynomials over finite fields, Curves over finite and local fields Applications of 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 \(x^n+y^m+1=0\) moduli space of curves; automorphisms; fiber type morphism; Hassett's moduli spaces Massarenti, A.; Mella, M., On the automorphisms of Hassett's moduli spaces, Trans. amer. math. soc., 369, 8879-8902, (2017) Families, moduli of curves (algebraic), Automorphisms of surfaces and higher-dimensional varieties, Fine and coarse moduli spaces, Stacks and moduli problems, Fibrations, degenerations in algebraic geometry On the automorphisms of Hassett's moduli 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 \(x^n+y^m+1=0\) Birch-Swinnerton-Dyer conjecture; Families of elliptic curves with large Tate-Shafarevich groups; Selmer group Kramer, K., A family of semistable elliptic curves with large Tate-Shafarevich groups, Proc. Amer. Math. Soc., 89, 379-386, (1983) Families, moduli of curves (algebraic), Elliptic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) A family of semistable elliptic curves with large Tate-Shafarevitch 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 \(x^n+y^m+1=0\) AK-invariant; locally nilpotent derivation; automorphism group of an algebra; automorphism group of affine hypersurface L. Makar-Limanov, On the group of automorphisms of a surface \(x^ny=P(z)\), Israel J. Math., 121 (2001), 113-123. Automorphisms of surfaces and higher-dimensional varieties, Automorphism groups of \(\mathbb{C}^n\) and affine manifolds, Hypersurfaces and algebraic geometry On the group of automorphisms of a surface \(x^ny= P(z)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 division algebras; anisotropic orthogonal involutions; Springer-Satz for orthogonal involutions; quadratic forms; motives of quadrics; function fields; Brauer-Severi varieties; Witt index; Chow motives А. С. Меркурьев, А. А. Суслин, \textit{K-когомологии многообpaзий Севери-Брауэра и гомоморфизм норменного вычета}, Изв. АН СССР, cep. мат \textbf{46} (1982), no. 5, 1011-1046. Engl. transl.: A. Merkurjev, A. Suslin, \textit{K-cohomology of Severi\(-\)Brauer varieties and the norm residue homomorphism}, Math. of the USSR-Izvestiya \textbf{21} (1983), 2, 307-340. Finite-dimensional division rings, Algebraic theory of quadratic forms; Witt groups and rings, Rings with involution; Lie, Jordan and other nonassociative structures, \(K\)-theory of quadratic and Hermitian forms, (Equivariant) Chow groups and rings; motives, Rational and birational maps On anisotropy of orthogonal involutions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 \(p\); tame coverings; fundamental group; graph of groups; semi-stable curves; Belyi's theorem; semi-stable Kummerian coverings Saïdi, M., Rev\hat etements modérés et groupe fondamental de graphe de groupes, Compositio Math., 107 (1997), 319-338. Coverings of curves, fundamental group, Coverings in algebraic geometry, Finite ground fields in algebraic geometry Tame coverings and the fundamental group of graphs of 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 \(x^n+y^m+1=0\) places of algebraic function fields; description of holomorphy ring of function fields; proof of Ax-Kochen-Ershov theorem; approximation theorems Kuhlmann, F. -V.; Prestel, A.: On places of algebraic function fields. J. reine angew. Math. 353, 181-195 (1984) General valuation theory for fields, Arithmetic theory of algebraic function fields, Model theory of fields, Transcendental field extensions, Real algebraic and real-analytic geometry, Model-theoretic algebra, Local ground fields in algebraic geometry Places of algebraic 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 \(x^n+y^m+1=0\) lemma of Seshadri; action of an algebraic group on an affine variety Popov, V. L.: On the ''lemma of Seshadri, Adv. soviet math. 8, 167-172 (1992) Group actions on varieties or schemes (quotients) On the ``Lemma of Seshadri''
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfeld quasi-modular forms; Hankel determinants; function fields of positive characteristic Modular forms associated to Drinfel'd modules, Global ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups Hankel-type determinants and Drinfeld quasi-modular forms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mickelsson-Faddeev cocycle; existence of string structures; bundle gerbe; quantum field theory; Atiyah-Patodi-Singer index theory; bundle of fermionic Fock spaces; gauge group action; Dixmier-Douady class; fermions in external fields; APS theorem; WZW model; Riemann surfaces; global Hamiltonian anomalies A. Alan Carey, A. Mickelsson, and M. Murray, ''Bundle gerbes applied to quantum field theory,'' hep-th/9711133. Quantum field theory; related classical field theories, Applications of global differential geometry to the sciences, Moduli problems for topological structures, Applications of PDEs on manifolds, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Generalizations of fiber spaces and bundles in algebraic topology Bundle gerbes applied to quantum field theory
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) action of adelic group; irreducible regular prehomogeneous vector space; Euler product; Euler factors; local zeta function; Bernstein-Sato polynomial Igusa J, On the arithmetic of a singular invariant,Am. J. Math. 110 (1988), 197--233 Zeta and \(L\)-functions in characteristic \(p\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) On the arithmetic of a singular invariant
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quartic Hessian surfaces; group of birational automorphisms; K3 surface; Leech lattice; Leech roots Dolgachev, [Dolgachev and Keum 02] I.; Keum, J., Birational automorphisms of quartic Hessian surfaces., \textit{Trans. Amer. Math. Soc.}, 354, 3031-3057, (2002) Birational automorphisms, Cremona group and generalizations, \(K3\) surfaces and Enriques surfaces, Automorphism groups of lattices, Automorphisms of surfaces and higher-dimensional varieties Birational automorphisms of quartic Hessian 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 \(x^n+y^m+1=0\) curves over function fields; canonical height; logarithmic discriminant Arithmetic varieties and schemes; Arakelov theory; heights, Algebraic functions and function fields in algebraic geometry Height inequality of nonisotrivial 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 \(x^n+y^m+1=0\) principally polarized abelian variety; theta function; Jacobian varieties of hyperelliptic curves and non-hyperelliptic curves; module over of ring of differential operators Cho K., Nakayashiki A., Differential structure of Abelian functions, Internat. J. Math., 2008, 19(2), 145--171 Theta functions and abelian varieties, Jacobians, Prym varieties, Relationships between algebraic curves and integrable systems Differential structure of abelian functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) characteristic \(p\); algebraic fundamental group of the affine line; Galois groups; Mathieu groups Shreeram S. Abhyankar, Mathieu group coverings and linear group coverings, Recent developments in the inverse Galois problem (Seattle, WA, 1993) Contemp. Math., vol. 186, Amer. Math. Soc., Providence, RI, 1995, pp. 293 -- 319. Coverings of curves, fundamental group, Separable extensions, Galois theory, Simple groups: alternating groups and groups of Lie type, Simple groups: sporadic groups Mathieu group coverings and linear group 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 \(x^n+y^m+1=0\) hypermap; automorphism groups of algebraic curves; triangular group; dessins d'enfants Singularities of curves, local rings, Enumerative problems (combinatorial problems) in algebraic geometry Representation theory of hypermaps and canonical models 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 \(x^n+y^m+1=0\) Weierstrass points; q-differentials; characteristic p; finiteness of automorphism group of curves Riemann surfaces; Weierstrass points; gap sequences, Local ground fields in algebraic geometry, Relationships between algebraic curves and integrable systems, Birational automorphisms, Cremona group and generalizations On higher-order Weierstrass points and the finiteness of the 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 \(x^n+y^m+1=0\) Birch--Swinnerton-Dyer conjecture; elliptic curves with complex multiplication; L-series; Mordell-Weil group; L-function B. H. Gross, ''On the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication,'' in Number Theory Related to Fermat's Last Theorem, Koblitz, N., Ed., Mass.: Birkhäuser, 1982, pp. 219-236. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Complex multiplication and moduli of abelian varieties, Elliptic curves over global fields, Special algebraic curves and curves of low genus On the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) ray class fields; global function fields; curves with many rational points; S-class numbers Auer, Roland, Ray class fields of global function fields with many rational places, Acta Arith., 95, 97-122, (2000) Arithmetic theory of algebraic function fields, Class field theory, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Finite ground fields in algebraic geometry, Algebraic number theory computations, Class numbers, class groups, discriminants Ray class fields of global function fields with many rational places
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cuspidal class number formula; modular curves; divisors; Siegel modular functions; group of modular units T. Takagi, The cuspidal class number formula for the modular curves \(X_{1}(3^{m})\), J. Math. Soc. Japan, 47 (1995), 671-686. Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Families, moduli of curves (analytic), Special algebraic curves and curves of low genus, Elliptic and modular units The cuspidal class number formula for the modular curves \(X_ 1(3^ m)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hasse-Witt matrix; p-rank of the divisor class group of algebraic function field of one variable; Cartier-Manin matrix T. Kodama: On the rank of the Hasse-Witt matrix. Proc. Japan Acad., 60A, 165-167 (1984). Algebraic functions and function fields in algebraic geometry, Analytic theory of abelian varieties; abelian integrals and differentials On the rank of Hasse-Witt matrix
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; double ramification cycle; quantum KdV; quantum tau function; Hurwitz numbers Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Deformation quantization, star products, Families, moduli of curves (algebraic) The quantum Witten-Kontsevich series and one-part double Hurwitz numbers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 with automorphisms; moduli space; mapping class group; Teichmüller space; Hurwitz monodromy vector; homological invariant; genus stabilization Catanese, F.; Lönne, M.; Perroni, F., Genus stabilization for the components of moduli spaces of curves with symmetries, Algebr. Geom., 3, 1, 23-49, (2016) Families, moduli of curves (analytic), Families, moduli of curves (algebraic), Complex-analytic moduli problems Genus stabilization for the components of moduli spaces of curves with symmetries
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) imperfect fields; inseparable extensions; function fields; reductive groups; absolutely simple groups; unipotent radicals; Weil restriction; Cartan subgroups; conjugacy theorems; Bruhat decompositions; linear algebraic groups; smooth connected affine groups Conrad, B., Gabber, O., Prasad, G.: Pseudo-reductive groups, new mathematical monographs: \textbf{17}, Cambridge Univ.~Press, Cambridge, pp. 533 +xix (2010) Linear algebraic groups over arbitrary fields, Structure theory for linear algebraic groups, Research exposition (monographs, survey articles) pertaining to group theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Other algebraic groups (geometric aspects), Affine algebraic groups, hyperalgebra constructions, Linear algebraic groups over local fields and their integers, Linear algebraic groups over global fields and their integers, Arithmetic theory of algebraic function fields Pseudo-reductive 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; covers; automorphisms; Galois groups; characteristic \(p\); lifting; Oort conjecture; simple group; almost simple; normal complement Finite automorphism groups of algebraic, geometric, or combinatorial structures, Coverings of curves, fundamental group, Separable extensions, Galois theory, Automorphisms of curves, Galois theory and commutative ring extensions, Formal methods and deformations in algebraic geometry Global Oort 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 \(x^n+y^m+1=0\) Deligne-Mumford stacks; Moduli of hyperelliptic curves; Picard group Families, moduli of curves (algebraic), Generalizations (algebraic spaces, stacks), Modular and Shimura varieties, Picard groups, Arithmetic ground fields for curves The stack of smooth hyperelliptic curves in characteristic two. (Le champ des courbes hyperelliptiques lisses en caractéristique deux)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 scheme of automorphisms; characteristic polynomial William C. Waterhouse, Automorphism group schemes of basic matrix invariants, Trans. Amer. Math. Soc. 347 (1995), no. 10, 3859 -- 3872. Birational automorphisms, Cremona group and generalizations, Determinants, permanents, traces, other special matrix functions, Group schemes, Finite-dimensional division rings, Actions of groups on commutative rings; invariant theory Automorphism group schemes of basic matrix invariants
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arrangements of hyperplanes; braid monodromy; curves with ordinary singularities; arrangement of real lines; fundamental group of the complement M. Salvetti,Arrangements of lines and monodromy of plane curves, Comp. Math.,68 (1988), pp. 103--122. Projective techniques in algebraic geometry, Singularities of curves, local rings, Coverings of curves, fundamental group, Coverings in algebraic geometry Arrangements of lines and monodromy of plane curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points; function fields; characteristic p; curves; abelian varieties Varieties over global fields, Arithmetic theory of algebraic function fields, Arithmetic varieties and schemes; Arakelov theory; heights, Global ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Bounds for the number of rational points on curves over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Diophant; affine algebraic curves; addition of abelian integrals; rational points on curves of third order И. Ц. Гохберг, А. А. Семенцул, Об обращении конечных теплицевых матриц и их континуальных аналогов,Мамем. исследования, Кишинев,7 (2) (1972), 201--223. History of Greek and Roman mathematics, History of mathematics in the 18th century, History of mathematics in the 19th century, History of number theory, History of algebraic geometry Diophant and 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 \(x^n+y^m+1=0\) elliptic curves over finite fields; bilinear complexity; finite field extension; complexity of bilinear multiplication; Chudnovsky algorithm; existence; optimal multiplication algorithm Shokrollahi, M. A.: Optimal algorithms for multiplication in certain finite fields using elliptic curves. Research Report, Universität Bonn; submitted for publication Number-theoretic algorithms; complexity, Elliptic curves, Analysis of algorithms and problem complexity Optimal algorithms for multiplication in certain finite fields using 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 \(x^n+y^m+1=0\) cohomology of finite Chevalley groups; cohomology stability; connected split reductive group scheme; change of fields; algebra retract; elementary abelian \(\ell \)-subgroups; cohomology algebras; integral cohomology; cohomological restriction map Friedlander, E.: Multiplicative stability for the cohomology of finite Chevalley groups. Comment. Math. Helv.63, 108--113 (1988). Erratum: Comment. Math. Helv.64, 348 (1989) Cohomology theory for linear algebraic groups, Linear algebraic groups over finite fields, Homology of classifying spaces and characteristic classes in algebraic topology, Group schemes, Cohomology of groups Multiplicative stability for the cohomology of finite 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 \(x^n+y^m+1=0\) Kronecker's limit formula; zeta-function of an order; Chowla-Selberg formula; elliptic curves Kaneko, M, A generalization of the chowla-Selberg formula and the zeta functions of quadratic orders, Proc. Jpn. Acad. Ser. A Math. Sci., 66, 201-203, (1990) Zeta functions and \(L\)-functions of number fields, Elliptic curves over global fields, Other algebras and orders, and their zeta and \(L\)-functions, Quadratic extensions, Elliptic curves A generalization of the Chowla-Selberg formula and the zeta functions of quadratic orders
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 Klein surface; group of automorphisms; HSK Coverings of curves, fundamental group, Group actions on varieties or schemes (quotients), Riemann surfaces, Fuchsian groups and their generalizations (group-theoretic aspects) On the automorphism groups of hyperelliptic 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 \(x^n+y^m+1=0\) exceptional polynomials; inverse Galois problem; Carlitz's conjecture; general exceptional covers; nonsingular projective algebraic curves; Schur covers; monodromy pair; modular curves over finite fields; fiber products; curves of high genus M. D. Fried, \textit{Global construction of general exceptional covers}, in Finite Fields: Theory, Applications, and Algorithms, Contemp. Math. 168, G. L. Mullen and P. J. Shiue, eds., AMS, Providence, RI, 1994, pp. 69--100. Finite fields (field-theoretic aspects), Coverings of curves, fundamental group, Curves over finite and local fields, Polynomials over finite fields, Hilbertian fields; Hilbert's irreducibility theorem, Varieties over finite and local fields, Inverse Galois theory, Varieties over global fields, Arithmetic theory of algebraic function fields, Families, moduli of curves (algebraic), Algebraic coding theory; cryptography (number-theoretic aspects) Global construction of general exceptional covers (with motivation for applications to encoding)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) towers of function fields; rational points; finite fields; hypergeometric functions; Deuring's polynomial Hasegawa, On asymptotically optimal towers over quadratic fields related to Gauss hypergeometric functions, Int. J. Number Theory 6 pp 989-- (2010) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Classical hypergeometric functions, \({}_2F_1\) On asymptotically optimal towers over quadratic fields related to Gauss hypergeometric functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(p\)-adic analogues of the Birch and Swinnerton-Dyer conjecture; Weil elliptic curves; extended Mordell-Weil group; \(p\)-adic height; \(p\)-adic multiplicative period Barry Mazur, John Tate & Jeremy Teitelbaum, ``On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer'', Invent. Math.84 (1986) no. 1, p. 1-48 Local ground fields in algebraic geometry, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over local fields, Arithmetic ground fields for curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Rational points On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) maximum number of rational points; genus-4 curves; small finite fields Howe, Everett W., New bounds on the maximum number of points on genus-4 curves over small finite fields, (Aubry, Y.; Ritzenthaler, C.; Zykin, A., Arithmetic, geometry, cryptography and coding theory, Contemp. math., vol. 574, (2012), American Mathematical Society Providence, RI), 69-86 Curves over finite and local fields, Finite ground fields in algebraic geometry, Rational points, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) New bounds on the maximum number of points on genus-4 curves over small 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 \(x^n+y^m+1=0\) generic matrices; stable rationality; fields of invariants; group algebras; lattices Beneish, E.: Induction Theorems on the center of the ring of generic matrices. Trans. Am. Math. Soc. 350(9), 3571--3585 (1998) Semiprime p.i. rings, rings embeddable in matrices over commutative rings, Actions of groups on commutative rings; invariant theory, Geometric invariant theory, Integral representations of finite groups, Group actions on varieties or schemes (quotients) Induction theorems on the stable rationality of the center of the ring of generic matrices
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(\ell\)-adic cohomology; independence of \(\ell \); grothendieck's trace formula; Lefschetz trace formula; zeta functions over finite fields; Euler-poincaré characteristic; Betti number; bloch's conductor conjecture; intersection cohomology; grothendieck's six operations; intermediate extension; Weil conjectures; Hodge polygon; Newton polygon; crystalline cohomology; Hodge filtration; coniveau filtration; alteration; Fano variety; rationally connected; Weil group; swan conductor; wild ramification; Brauer trace; log scheme; logarithmic differential forms; Čebotarev's density theorem; semisimple group; fatou's Lemma Illusie, L.: Miscellany on traces in \(\mathcall \)-adic cohomology: a survey. Japan J. Math. \textbf{1}(1), 107-136 (2006). Erratum: Japan J. Math. \textbf{2}(2), 313-314 (2007) Étale and other Grothendieck topologies and (co)homologies, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Linear algebraic groups over arbitrary fields Miscellany on traces in \(\ell\)-adic cohomology: a survey
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) irrational involutions; automorphisms of curves Automorphisms of curves, History of mathematics in the 20th century, History of algebraic geometry De Franchi's contributions to the theory 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 \(x^n+y^m+1=0\) SDP-Hopf algebra; Lie algebra; smooth formal group (law); co(ntra)variant bialgebra; sequence of divided powers; primitive element; pure primitive; curve; symmetric function; quasisymmetric function; noncommutative symmetric function; composition; Lyndon composition Symmetric functions and generalizations, Formal groups, \(p\)-divisible groups, Hopf algebras and their applications Various \(S\)-adic symmetric functions and smooth formal 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 \(x^n+y^m+1=0\) relative homology groups of the Fermat curves; adelic beta function; hyperadelic gamma function Anderson, G. W.: The hyperadelic gamma function: A précis. Adv. stud. Pure math. 12, 1-19 (1987) Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Curves over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) The hyperadelic gamma function: a précis
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; group of points; effective addition law General structure theorems for groups, Elliptic curves A survey on the group of points arising from elliptic curves with a Weierstrass model over a 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 \(x^n+y^m+1=0\) automorphisms of curves; non-split Cartan modular curves Modular and Shimura varieties, Automorphisms of curves Constraints on the automorphism group of a 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 \(x^n+y^m+1=0\) quaternion algebra; Brauer group; pseudoglobal field; function field of genus zero; Hasse principle Quaternion and other division algebras: arithmetic, zeta functions, Brauer groups (algebraic aspects), Brauer groups of schemes Quaternion algebras over a pseudoglobal 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 \(x^n+y^m+1=0\) local fields; irreducible algebraic varieties; rationality problem for group varieties; semisimple algebraic groups; almost simple algebraic groups; number fields; global function fields; Tits indices Linear algebraic groups over arbitrary fields, Rational and unirational varieties, Group varieties, Rational points, Local ground fields in algebraic geometry On the problem of rational group 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 \(x^n+y^m+1=0\) Weil reciprocity; class field theory; algebraic curves; function fields; residues Algebraic functions and function fields in algebraic geometry, Symbols and arithmetic (\(K\)-theoretic aspects), Class field theory Adelic and idelic pairings related to Weil reciprocity on 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 \(x^n+y^m+1=0\) Deligne-Mumford compactification; moduli of curves; stack; mapping class group; orbit category Ebert, J; Giansiracusa, J, On the homotopy type of the Deligne-Mumford compactification, Algebr. Geom. Topol., 8, 2049-2062, (2008) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Generalizations (algebraic spaces, stacks), Fine and coarse moduli spaces, Teichmüller theory for Riemann surfaces On the homotopy type of the Deligne-Mumford compactification
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) survey; integral indefinite quadratic forms; discriminant forms; representations of one form by another; group of motions of the n- dimensional hyperbolic space; discrete subgroup; reflections; crystallographic group; surface singularities; automorphisms of algebraic K3-surfaces I. Dolgachev, \textit{Integral quadratic forms: applications to algebraic geometry (after V. Nikulin)}, \textit{Séminaire Bourbaki}\textbf{25} (1982) 251. Quadratic forms over global rings and fields, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Discrete subgroups of Lie groups, Classical groups, Singularities of surfaces or higher-dimensional varieties, Singularities in algebraic geometry, Other geometric groups, including crystallographic groups Integral quadratic forms: applications to algebraic geometry (after V. Nikulin)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) classification of germs; plane curves; finite determinacy; vector fields Singularities of curves, local rings Curves in a foliated plane
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; Bombieri-lang conjecture; varieties of general type Rational points, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Rational points of varieties with ample cotangent bundle 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 \(x^n+y^m+1=0\) correspondences on hyperbolic curves; automorphisms of Teichmüller space S. Mochizuki, Correspondences on hyperbolic curves. Preprint, available at http://www.kurims.kyoto-u.ac.jp/ motizuki/papers-english.html MR1637015 Automorphisms of curves, Coverings of curves, fundamental group, Isogeny, Families, moduli of curves (algebraic), Teichmüller theory for Riemann surfaces Correspondences on hyperbolic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curve; Heron triangle; specialization; Diophantine triple; family of elliptic curves; torsion group Elliptic curves, Elliptic curves over global fields On elliptic curves via heron triangles and Diophantine triples
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) torsion group; elliptic curves; cubic fields Najman, F.: Torsion of rational elliptic curves over cubic fields and sporadic points on \(X1(n)\), (2012) Elliptic curves over global fields, Arithmetic aspects of modular and Shimura varieties, Cubic and quartic extensions, Elliptic curves Torsion of elliptic curves over cubic 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 \(x^n+y^m+1=0\) divisor class group of affine surface P. Blass and J. Lang , A method for computing the kernel of a map of divisor classes of local rings in characteristic p \neq 0 , Mich. Math. J. 35 (1988). Regular local rings, Divisors, linear systems, invertible sheaves, Special surfaces A method for computing the kernel of a map of divisor classes of local rings in characteristic p\(\neq 0\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quadratic differential system; algebraic invariant curve; topological equivalence; group action; affine invariant polynomial; configuration of invariant lines; multiplicity of an invariant line; Lotka-Volterra differential system Schlomiuk, D; Vulpe, N, Global classification of the planar Lotka-Volterra differential systems according to their configurations of invariant straight lines, J. Fixed Point Theory Appl., 8, 69, (2010) Nonlinear differential equations in abstract spaces, Geometric methods in ordinary differential equations, Group actions on varieties or schemes (quotients), Symmetries, invariants of ordinary differential equations, Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems Global classification of the planar Lotka-Volterra differential systems according to their configurations of invariant straight lines
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) class numbers; function fields; mean values of \(L\)-functions Andrade, J. C., A note on the mean value of \textit{L}-functions in function fields, Int. J. Number Theory, 8, 7, 1725-1740, (2012) Class numbers, class groups, discriminants, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) A note on the mean value of \(L\)-functions in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global fields; Drinfeld modules; elliptic curves; distribution of primes; densities Drinfel'd modules; higher-dimensional motives, etc., Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Complex multiplication and abelian varieties On the distribution of torsion points modulo primes: the case 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 \(x^n+y^m+1=0\) Galois group; projective symplectic group; unramified covering of the affine line; quintinomial equations; one punctured affine line Shreeram, S. Abhyankar, and, Paul, A. Loomis, Twice more nice equations for nice groups, to appear. Separable extensions, Galois theory, Coverings of curves, fundamental group, Extensions, wreath products, and other compositions of groups, Simple groups: alternating groups and groups of Lie type Twice more nice equations for nice 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 \(x^n+y^m+1=0\) elliptic curves; function fields; Birch-Swinnerton-Dyer conjecture; modular elements; modular forms; special values; \(L\)-functions; Mazur and Tate's refined conjectures; integrality; functional equation Tan K.-S., Modular elements over function fields, J. Number Theory 45 (1993), no. 3, 295-311. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Modular elements 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 \(x^n+y^m+1=0\) discriminant of splitting fields of principal homogeneous spaces; finiteness for the Tate-Shafarevich group of an elliptic curve; Arakelov intersection theory; effective divisor; Faltings Riemann-Roch theorem Paul Hriljac, Splitting fields of principal homogeneous spaces , Number theory (New York, 1984-1985), Lecture Notes in Math., vol. 1240, Springer, Berlin, 1987, pp. 214-229. Special algebraic curves and curves of low genus, Riemann-Roch theorems, Homogeneous spaces and generalizations, Elliptic curves, Divisors, linear systems, invertible sheaves Splitting fields of principal homogeneous spaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) inverse problem of Galois theory, algebraic function field; arithmetic fundamental group; algebraic fundamental group; special linear group; SL(2,q); Mathieu group; \(M_{12}\); \(M_{22}\) Matzat, B.H.: Zwei Aspekte konstruktiver Galoistheorie,J. Algebra 96 (1985), 499--531 Galois theory, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Finite simple groups and their classification, Simple groups: sporadic groups, Coverings in algebraic geometry Zwei Aspekte konstruktiver Galoistheorie. (Two aspects of constructive Galois theory)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) biholomorphic automorphisms; affine Nash group [Z1]Zaitsev, D., On the automorphism groups of algebraic bounded domains.Math. Ann., 302 (1995), 105--129. Automorphisms of curves, Nash functions and manifolds, Complex Lie groups, group actions on complex spaces, Semialgebraic sets and related spaces On the automorphism groups of algebraic bounded 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 \(x^n+y^m+1=0\) noncommutative tori; real multiplication; Stark numbers; real quadratic fields; spectral triples; noncommutative boundary of modular curves; modular shadows; quantum statistical mechanics Noncommutative topology, Relations with noncommutative geometry, Noncommutative geometry (à la Connes), Quantum dynamics and nonequilibrium statistical mechanics (general), Noncommutative algebraic geometry Noncommutative geometry and arithmetic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(p\)-extensions of algebraic function fields; Artin-Schreier theory; characteristic \(p\); genus; number of rational points; coding theory; gap number Arnaldo Garcia and Henning Stichtenoth, Elementary abelian \(p\)-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67--79. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves Elementary abelian \(p\)-extensions of algebraic 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; discrete logarithm; finite abelian groups; cryptosystems; jacobians of hyperelliptic curves; finite fields; groups of almost prime order N. Koblitz, Hyperelliptic cryptosystems, J. Cryptology 1 (1989), no. 3, 139-150. Cryptography, Jacobians, Prym varieties, Finite ground fields in algebraic geometry Hyperelliptic cryptosystems
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(K_ 2\) of fields; Brauer group; cyclic algebras; generators A. S. Merkurjev, Structure of the Brauer group of fields , Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 4, 828-846, 895, trad. anglaise, Math. USSR-Izv. 27 (1986), 141-157. Skew fields, division rings, Brauer groups of schemes, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Galois cohomology On the structure of the Brauer group of a 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 \(x^n+y^m+1=0\) construction; curves over finite fields; characteristic 2; supersingular curves; coding theory; generalized Hamming weights; odd characteristics; number of parameters G. VAN DER GEER - M. VAN DER VLUGT, On the existence of supersingular curves of given genus, J. Reine Angew. Math., 458 (1995), pp. 53-61. Zbl0819.11022 MR1310953 Curves over finite and local fields, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry On the existence of supersingular curves of given genus
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Automorphism of function fields; singular points; rational function fields. Automorphisms of curves, Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry A relation between Galois automorphism and curve singularity
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic geometry; uniformly bounded p-torsion of elliptic curves; order of group of p-torsion points Manin, Ju. I., The \textit{p}-torsion of elliptic curves is uniformly bounded, Izv. Akad. Nauk SSSR Ser. Mat., 33, 459-465, (1969) Elliptic curves Uniformly bounded \(p\)-torsion of elliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curves over function fields; Birch and Swinnerton-Dyer conjecture Hauer H. and Longhi I., Teitelbaum's exceptional zero conjecture in the function field case, J. reine angew. Math. 591 (2006), 149-175. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Teitelbaum's exceptional zero conjecture in the function field case
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) descent on elliptic curves; invariants of binary quartics; group of rational points; elliptic curve; algorithm; Mordell-Weil group --------, Classical invariants and \(2\)-descent on elliptic curves , J. Symbolic Comput., 31 (2001), 71-87. Elliptic curves over global fields, Elliptic curves, Computer solution of Diophantine equations Classical invariants and 2-descent on elliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois point; plane curve; birational transformation; automorphism group Miura, K; Ohbuchi, A, Automorphism group of plane curve computed by Galois points, Beiträge zur Algebra und Geometrie, 56, 695-702, (2015) Automorphisms of curves, Plane and space curves Automorphism group of plane curve computed by Galois 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 \(x^n+y^m+1=0\) field of moduli; field of definition; automorphism group Kontogeorgis, Aristides, Field of moduli versus field of definition for cyclic covers of the projective line, J. Théor. Nombres Bordeaux, 21, 3, 679-692, (2009) Coverings of curves, fundamental group, Automorphisms of curves, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Field of moduli versus field of definition for cyclic covers of the projective line
| 1 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curve over a finite field; zeta function; maximal curve; minimal curve Anuradha, N.: Zeta function of the projective curve ay2l=bX2l+cZ2l over a class of finite fields, for odd primes l, Proc. indian acad. Sci. math. Sci. 115, No. 1, 1-14 (2005) Curves over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Arithmetic ground fields for curves Zeta function of the projective curve \(aY^{2l}= bX^{2l}+ cZ^{2l}\) over a class of finite fileds, for odd primes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer group; field of rational functions; reciprocity law; projective curve Brauer groups of schemes, Arithmetic theory of algebraic function fields, Varieties over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry Reciprocity laws for simple algebras over function fields of number curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cubic function field; discriminant; non-singularity; integral basis; signature of a place; class number DOI: 10.4153/CJM-2010-032-0 Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Special algebraic curves and curves of low genus, Curves over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Cubic and quartic extensions, Class numbers, class groups, discriminants, Applications to coding theory and cryptography of arithmetic geometry An explicit treatment of cubic function fields with applications
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Contou-Carrère symbol; Weil reciprocity law Fernando Pablos Romo, A Contou-Carrère symbol on \?\?(\?,\?((\?))) and a Witt residue theorem on \Cal M\?\?(\?,\Sigma _{\?}), Int. Math. Res. Not. (2006), Art. ID 56824, 21. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Symbols and arithmetic (\(K\)-theoretic aspects), Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields A Contou-Carrère symbol on \(\text{Gl}(n,A((t)))\) and a Witt residue theorem on \(\text{Mat}(n,\Sigma_C)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; strongly normal; weakly normal; movable singularity Abstract differential equations, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Singularities of curves, local rings Movable singularities and differential Galois theory
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) abstract elliptic function fields; automorphisms; meromorphisms; addition theorem Hasse, H.: Zur theorie der abstrakte elliptischen funktionenkörper. II. automorphismen und meromorphismen. Das additionstheorem. J. reine angrew. Math. 175, 69-88 (1936) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Theorie der abstrakten elliptischen Funktionenkörper. II: Automorphismen und Meromorphismen. Das Additionstheorem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational function field; automorphism group; Ree group; Hasse-Weil bound Pedersen, J.P.: A function field related to the Ree group. In: Coding Theory and Algebraic Geometry, Lecture Notes in Mathematics, vol. 1518, pp. 122--132. Springer, Berlin (1992) Arithmetic theory of algebraic function fields, Simple groups, Algebraic functions and function fields in algebraic geometry A function field related to the Ree 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 \(x^n+y^m+1=0\) algorithms; computation in the Jacobian of a hyperelliptic curve D. G. Cantor, \textit{Computing in the Jacobian of a hyperelliptic curve}, Math. Comp., 48 (1987), pp. 95--101, . Jacobians, Prym varieties, Software, source code, etc. for problems pertaining to algebraic geometry, Software, source code, etc. for problems pertaining to field theory, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Special algebraic curves and curves of low genus Computing the Jacobian of a hyperelliptic 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 \(x^n+y^m+1=0\) algebraic function field; Hasse-Witt invariants; Deuring-Shafarevich formula; Galois group; maximal unramified p-extension; p-profinite completion Arithmetic theory of algebraic function fields, Ramification and extension theory, Galois theory, Algebraic functions and function fields in algebraic geometry The Deuring-Šafarevič formula revisited
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cyclotomic function fields; algebraic curve over a finite field; \(L\)-functions Goss, D., On a new type of \textit{L}-functions for algebraic curves over finite fields, Pacific J. math., 105, 143-181, (1983) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On a new type of \(L\)-function for algebraic curves over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of non-rational subfields; number of separable subfields; number of morphisms of algebraic curves; Chow coordinates; theorem of the base; Jacobian; genus; function field; Angle theorem; de Franchis' theorem E. Kani, Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. Zbl0615.12017 MR842053 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Birational geometry, Jacobians, Prym varieties, Divisors, linear systems, invertible sheaves, Special surfaces Bounds on the number of non-rational subfields 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 \(x^n+y^m+1=0\) algebraic function fields; valuation; value group; rank; direct sum of n infinite cyclic groups MacLane, S. - Schilling, O.F.G.\(\,\): Zero-dimensional branches of rank 1 on algebraic varieties, Annals of Math. 40 (1939), 507-520 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Valued fields Zero-dimensional branches of rank one on 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 \(x^n+y^m+1=0\) DOI: 10.1007/s00574-004-0008-9 Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Thue-Mahler equations, Finite ground fields in algebraic geometry On towers of function fields of Artin-Schreier type
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) subrational; unirational; subruled; uniruled; ruled fields; ruling; generalized Lüroth theorem; Samuel problem; Zariski problem; separability Jack Ohm, On ruled fields, Sém. Théor. Nombres Bordeaux (2) 1 (1989), no. 1, 27 -- 49 (English, with French summary). Transcendental field extensions, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On ruled 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 \(x^n+y^m+1=0\) number theory Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Power series representing algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tomašić, I.: A twisted theorem of chebotarev, C. R. Acad. sci. Paris, ser. I 347, 385-388 (2009) Arithmetic theory of algebraic function fields, Density theorems, Algebraic functions and function fields in algebraic geometry A twisted theorem of Chebotarev
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 groups; automorphism groups of function fields; hyperelliptic function-field R. Brandt, Über die Automorphismengruppen von algebraischen Funktionenkörpern, PhD thesis, Universität Essen, 1988. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On the groups of automorphisms of algebraic 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 \(x^n+y^m+1=0\) automorphism groups of algebraic function fields; realization of group as Galois group; Galois theory Separable extensions, Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Representations of groups as automorphism groups of algebraic systems Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Gauss conjecture; modular curves; Drinfeld modular curves; class field tower; congruence function fields; ring of \(S\)-integers; ideal class number; class number Lachaud, G.; Vladut, S.: Gauss problem for function fields, J. number theory 85, No. 2, 109-129 (2000) Arithmetic theory of algebraic function fields, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Class field theory, Finite ground fields in algebraic geometry, Jacobians, Prym varieties, Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Curves over finite and local fields Gauss problem 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 \(x^n+y^m+1=0\) valued function fields; genus change; algebraic function field; reduction of constants; rigid analytic geometry; non-discrete valuation Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Non-Archimedean valued fields, Arithmetic ground fields for surfaces or higher-dimensional varieties Genre des corps de fonctions values après Deuring, Lamprecht et Mathieu. (Genus of valued function fields after Deuring, Lamprecht and Mathieu)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) towers of function fields; Drinfeld modules; curves with many points Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Arithmetic theory of algebraic function fields, Computational aspects of algebraic curves Good towers of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Fermat curve over \({\mathbb{Q}}\); integral differentials; birational invariants; discrete valuation rings Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On certain birational invariants of the Fermat curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Differentiation of algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; domain of regularity; Hilbert's irreducibility theorem Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Über die Kennzeichnung algebraischer Funktionenkörper durch ihren Regularitätsbereich
| 0 |
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