text
stringlengths
2
1.42k
label
int64
0
1
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) computational geometry; basic semi-algebraic sets; convexity; semidefinite programming Lasserre J.B.: Certificates of convexity for basic semi-algebraic sets. Appl. Math. Lett. 23(8), 912--916 (2010)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) displays; \(p\)-divisible groups; Dieudonne modules; algebraic stacks Lau, E, Smoothness of the truncated display functor, J. Am. Math. Soc., 26, 129-165, (2013)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Ulrich bundles; Frobenius split varieties; abelian varieties; \(K3\) surfaces; surfaces of general type; threefolds; Fano varieties
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Kloosterman sum; Kloostermann sheaves; Monodromy; Hyper-Kloosterman sum; Generalized Kloosterman sum; Bilinear form; Type-II sum; Type-I sum; Moments; Twisted cuspidal \(L\)-functions
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) non-commutative Chow motive; Grothendieck group; semi-simplicity M. Marcolli and G. Tabuada, Noncommutative motives, numerical equivalence, and semi-simplicity, Amer. J. Math. 136 (2014), no. 1, 59-75.
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) semi-stable representations; Witt vectors; crystalline cohomology; characteristic \(p\); crystalline representations of the absolute Galois group; Hodge-Tate weights Breuil, Christophe, Construction de représentations \textit{p}-adiques semi-stables, Ann. Sci. Éc. Norm. Supér., 31, 281-327, (1998)
1
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) filtered module; strongly divisible module Breuil, Christophe, Représentations semi-stables et modules fortement divisibles, Invent. Math., 136, 1, 89-122, (1999)
1
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) \(p\)-adic representations; \(p\)-adic Hodge theory; Breuil modules Caruso, Xavier, Représentations semi-stables de torsion dans le case \(e r < p - 1\), J. Reine Angew. Math., 594, 35-92, (2006)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) \((\phi,\tau)\)-module; semi-stable representation; Galois representation; \(E(u)\)-height Caruso, X., Représentations galoisiennes \textit{p}-adiques et (\(######\)modules, Duke Math. J., 162, 13, 2525-2607, (2013)
1
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) crystalline cohomology; \(p\)-adic cohomology; characteristic \(p\); vanishing \(p\)-adic cycles; de Rham cohomology; comparison theorems BREUIL (C.) . - Cohomologie étale de p-torsion et cohomologie cristalline en réduction semi-stable , en préparation.
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Torsion Galois representations; semi-stable representations; norm field theory Caruso, X.; Savitt, D., Polygons de Hodge, de Newton et de línertie moderee des representations semi-stables, Math. Ann., 343, 773-789, (2009)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) \(p\)-adic Hodge theory; semi-stable representations Liu, T., Torsion \textit{p}-adic Galois representations and a conjecture of Fontaine, Ann. Sci. Éc. Norm. Supér. (4), 40, 4, 633-674, (2007)
1
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) semi-stable representations; integral \(p\)-adic Hodge theory; Kisin-modules 10. Liu, Tong A note on lattices in semi-stable representations \textit{Math. Ann.}346 (2010) 117--138 Math Reviews MR2558890
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Serre weights; Galois representations; Hilbert modular forms T. Gee and D. Savitt, Serre weights for mod \textit{p} Hilbert modular forms: The totally ramified case, J. reine angew. Math. 660 (2011), 1-26.
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Čech cohomology; crystalline cohomology; Witt vectors; logarithmic point; monodromy operator; log-crystalline cohomology; syntomic coverings Breuil, C.: Log-syntomic topology, log-crystalline cohomology and cech cohomology. Bulletin de la soc. Mathématique de France 124, 587-647 (1996)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) modular Galois representation; weight; Hecke-operator; unitary group; p-adic Hodge theory Caruso, X., David, A., Mézard, A.: Un calcul d'anneaux de déformations potentiellement Barsotti-Tate. Trans. Am. Math. Soc. arXiv:1402.2616 (\textbf{to appear})
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) good reduction of a curve; Fontaine's rings; crystalline site; unipotent fundamental group F.~Andreatta, A.~Iovita, and M.~Kim, \emph{A \(p\)-adic non-abelian criterion for good reduction of curves}, Duke Math. J. \textbf{164} (2015), no.~13, 2597--2642. DOI 10.1215/00127094-3146817; zbl 1347.11051; MR3405595
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Hodge polygon; tame inertia weight; Breuil module; ramification; \(p\)-adic Galois representation Caruso, X., Savitt, D.: Poids de l'inertie modérée de certaines représentations cristallines, en préparation
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) potentially semi-stable representations; filtered \((\varphi,N)\)-modules; Kisin modules Liu, T., Lattices in filtered (\({\phi}\), \textit{N})-modules, J. Inst. Math. Jussieu 2, 11, 3, 659-693, (2012)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) modular forms; Serre's conjecture; crystalline representations; Kisin modules; Breuil modules Gee, T.; Liu, T.; Savitt, D., The weight part of Serre's conjecture for \(\operatorname{GL}(2)\), Forum Math. Pi, 3, (2015)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Selmer groups; Galois representations; lattices in crystalline representations; Bloch-Kato finite cohomology; strongly divisible modules Iovita, Adrian; Marmora, Adriano, On the continuity of the finite Bloch-Kato cohomology, Rend. Semin. Mat. Univ. Padova, 134, 239-271, (2015), MR 3428419
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) modular representation; Serre conjecture; Serre weight; unitary group 5. Gee, Toby and Liu, Tong and Savitt, David The Buzzard-Diamond-Jarvis conjecture for unitary groups \textit{J.~Amer. Math. Soc.}27 (2014) 389--435 Math Reviews MR3164985
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Caruso, Xavier, Conjecture de l'inertie modérée de Serre, Invent. Math., 171, 3, 629-699, (2008)
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Galois representations; Serre weights; quaternion algebras; Breuil modules Toby Gee, Florian Herzig & David Savitt, ''General Serre weight conjectures'', preprint, , 2015
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Fontaine theory; Breuil-Kisin modules; Dieudonné modules; Hodge structures Alain Genestier & Vincent Lafforgue, ''Chtoucas restreints pour les groupes réductifs et paramétrisation de Langlands locale'', en préparation
0
semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality Breuil, C., Représentations \textit{p}-adiques semi-stables et transversalité de Griffiths, Math. Ann., 307, 191-224, (1997) Galois representations; Mumford-Tate group; abelian varieties DOI: 10.1007/s00208-004-0514-5
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Picard numbers; rank of the Mordell-Weil group; elliptic curves over function fields; automorphisms Peter F. Stiller, The Picard numbers of elliptic surfaces with many symmetries, Pacific J. Math. 128 (1987), no. 1, 157 -- 189.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) inverse Galois theory; algebraic fundamental group; plane curves; factorization of polynomials; resolution of plane curve singularities; hyperelliptic function fields; construction of Galois extensions; finite group; Galois group; PSL(2,8); unramified covering; affine line Shreeram S. Abhyankar, Square-root parametrization of plane curves, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 19 -- 84.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) number of rational points; Deligne-Lusztig curves; function fields; large groups of automorphisms; Goppa codes HP Johan~P. Hansen and Jens~Peter Pedersen, \emph Automorphism groups of Ree type, Deligne-Lusztig curves and function fields, J. Reine Angew. Math. \textbf 440 (1993), 99--109.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) affine space; polynomials over finite fields; linearized polynomial; group of polynomial automorphisms; group of tame automorphisms Joost Berson, Derivations of polynomial rings over a domain, Master's thesis, University of Nijmegen, June 1999.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic surfaces; elliptic curves over function fields; generators of Mordell-Weil group; Kodaira-Néron model; number of minimal sections; specialization homomorphisms
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) fields of large transcendence degree; algebraic independence; zero lemmas; zero estimate for group varieties; primary ideal; polynomial rings; algebraic subgroups of products of elliptic curves; effective version of Hilbert's Nullstellensatz; Kolchin theorem; Weierstrass elliptic function Masser, D. W.; Wüstholz, G., Fields of large transcendence degree generated by values of elliptic functions, Invent. Math., 72, 3, 407-464, (1983)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) polynomial automorphisms; tame automorphisms; affine spaces over finite fields; automorphism group; bijections; set of zeros; primitive subgroup of the symmetric group S. Maubach, Polynomial automorphisms over finite fields, Serdica Math. J. 27 (2001), no. 4, 343--350.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 1996.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) diophantine equations; Siegel's theorem; integral points on affine curves; function-fields of characteristic zero José Felipe Voloch, Siegel's theorem for complex function fields, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1307 -- 1308.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) abstract elliptic function fields; divisor class group of finite order; automorphisms; meromorphisms; addition theorems; structure of ring of meromorphisms; Riemann hypothesis
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic curves; algebraic function fields; maximal curves; maximal function fields; automorphisms of function fields Güneri, C.; Özdemir, M.; Stichtenoth, H., The automorphism group of the generalized giulietti-korchmáros function field, \textit{Adv. Geom.}, 13, 369-380, (2013)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic groups; adjoint groups; R-equivalence; nondyadic local fields; function fields of curves; algebras with involution; Hermitian forms; Rost invariant R. Preeti and A. Soman, Adjoint groups over \Bbb Q_{\?}(\?) and R-equivalence, J. Pure Appl. Algebra 219 (2015), no. 9, 4254 -- 4264.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Hasse-Weil-Serre bound; zeta function of curves over finite fields; rational points K. Lauter, Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields, Institut de Mathématiques de Luminy, preprint, 1999, pp. 99--29.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) hyperbolic fibre space; higher dimensional analogue of Mordell's conjecture for curves; hyperbolic manifolds; algebraic families of hyperbolic varieties; Mordell's conjecture over function fields Noguchi, J.Hyperbolic fiber spaces and Mordell's conjecture over function fields, Publ. Research Institute Math. Sciences Kyoto University21, No. 1 (1985), 27--46.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) arithmetic function; number of factorizations of an integer; group of rational points; 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) 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
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) conjecture of Beilinson and Bloch; rank of the Griffiths group; smooth projective variety over a number field; order of vanishing of an L-function; elliptic curves J. Buhler, C. Schoen, and J. Top, ''Cycles, \(L\)-functions and triple products of elliptic curves,'' J. reine angew. Math., vol. 492, pp. 93-133, 1997.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) deformation theory; finite group schemes; abelian varieties; Newton polygons; automorphisms 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) 2-dimensional Cremona group; algebraic automorphism; automorphism of the rational function field; birational automorphisms D. Wright, Two-dimensional Cremona groups acting on simplicial complexes, Trans. Amer. Math. Soc. 331 (1992), no. 1, 281--300.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) function fields; Brauer group; theorem of Davenport-Halberstam Serre, Jean-Pierre, Spécialisation des éléments de \(\operatorname{Br}_2(\mathbf{Q}(T_1, \ldots, T_n))\), C. R. Acad. Sci. Paris, Sér. I, 311, 7, 397-402, (1990)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic function fields; constructions of linear codes; algebraic curves; algebraic-geometric codes; Goppa codes Ferruh Özbudak and Henning Stichtenoth, Constructing codes from algebraic curves, IEEE Trans. Inform. Theory 45 (1999), no. 7, 2502 -- 2505.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) function fields; biquadratic curves; biquadratic covers; number of points over finite fields; arithmetic statistics
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) automorphism groups of algebraic function fields; realization of group as Galois group; 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) 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)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) towers of function fields; Drinfeld modules; curves with many points
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) rational points of affine variety; Hasse principle; ring of all algebraic integers; capacity theory on algebraic curves; completely valued algebraically closed fields; Hilbert's tenth problem; decision procedure for diophantine equations Rumelv, R. S., Arithmetic over the ring of all algebraic integers, Journal für die Reine und Angewandte Mathematik, 368, 127-133, (1986)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Hasse principle; function fields of \(p\)-adic curves Parimala, R.: A Hasse principle for quadratic forms over function fields. Bull. amer. Math. soc. (N.S.) 51, No. 3, 447-461 (2014)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic function fields; holomorphic semisimple differentials; p- extensions of \({\mathbb{Z}}_ pfields\) of CM-type; p-class group G. Villa and M. Madan,Structure of semisimple differentials and p-class groups in \(\mathbb{Z}\) p -extensions. Manuscripta Mathematica57 (1987), 315--350.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) function fields; plane curves of genus one; exceptional points Nagell, T.: [3] ''Les points exceptionnels sur les cubiques planes du premier genre'', II, ibid. Nova Acta Reg. Soc. Sci. Upsaliensis, Ser. IV, 14, 1946, No. 3.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) two dimensional global fields; algebraic function field in one; variable over algebraic number field; Galois cohomology group; \(H^ 3\); Hasse principles; local-global principles; reduced norms; division algebras; quadratic forms; sum of squares K.~Kato, {A {H}asse principle for two dimensional global fields. With an appendix by {J}.-{L} {C}olliot-{T}hélène.}, J. Reine Angew. Math. {366} (1986), 142--180. DOI 10.1515/crll.1986.366.142; zbl 0576.12012; MR0833016
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Chowla's conjecture; \(L\)-functions; zeta functions of curves; Carlitz extensions; cyclotomic function fields; abelian varieties over finite fields
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) finite field; finite group of automorphisms; Artin L-function; total degree
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) hyperplane section of curve; curves on hyperplanes; Galois group of function field; incidence; trisecant lemma E. Ballico, On the general hyperplane section of a curve in char. p, Rendiconti Istit. Mat. Univ. Trieste 22 (1990), 117--125.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) affine algebras; actions of finite dimensional cocommutative Hopf algebras; Noether's theorem; finite groups of automorphisms; triangular Hopf algebras; quantum-commutative modules; non-commutative determinant functions; symmetric braidings; twist maps; categories of modules; Grassmann algebras; group gradings Cohen, M.; Westreich, S.; Zhu, S., Determinants, integrality and Noether's theorem for quantum commutative algebras, Israel J. math., 96, 185-222, (1996)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) valuation rings of function fields; coordinate ring of affine; variety over a real closed field; prime cone
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Frobenius group; monodromy group; coverings of curves; algebraic 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) canonical module; ring of invariants; reductive group; affine variety; generating function Knop, F., Der kanonische modul eines invariantenringes, J. Algebra, 127, 40-54, (1989)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic surface in projective space; function fields of surfaces; subfields of function fields of algebraic surfaces; dominant rational maps; plane curves Lee, Y; Pirola, G, On subfields of the function field of a general surface in \({\mathbb{P}}^3\), Int. Math. Res. Not., 24, 13245-13259, (2015)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) quadratic function field; quadratic number field; ideal class group; algorithm; Jacobian; hyperelliptic curve; concordant ideals; g-adic numbers; elliptic function fields; elliptic curves; 2-descent Hellegouarch, Y.: Algorithme pour calculer LES puissances successives d'une classe d'idéaux dans uns corps quadratique. Application aux courbes elliptiques. C. R. Acad. sci. Paris sér. I 305, 573-576 (1987)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) abelian variety; function fields of curves; heights; Néron model
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) central division algebras; cyclic algebras; ramification; curve points; nodal points; Brauer groups; curves over local fields; \(p\)-adic curves; field extensions; algebraic function fields; curves over rings of integers of \(p\)-adic fields D. J. Saltman, ''Cyclic algebras over \(p\)-adic curves,'' J. Algebra, vol. 314, iss. 2, pp. 817-843, 2007.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Riemann hypothesis in function-fields; algebro-geometric theory of curves and their correspondences Weil, André, Sur les courbes algébriques et les variétés qui s'en déduisent, Actual. Sci. Ind., vol. 1041, (1948), Hermann et Cie: Hermann et Cie Paris
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) field of characteristic zero; affine plane curves; automorphism group Daniel Daigle, On locally nilpotent derivations of \?[\?\(_{1}\),\?\(_{2}\),\?]/(\?(\?)-\?\(_{1}\)\?\(_{2}\)), J. Pure Appl. Algebra 181 (2003), no. 2-3, 181 -- 208.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) group representations on Riemann-Roch spaces; automorphisms of curves
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) abstract elliptic function fields; divisor class group of finite order Hasse, H., Zur theorie der abstrakten elliptischen funktionenkörper. I. die struktur der gruppe der divisorenklassen endlicher ordnung, J. Reine Angew. Math., 1936, 175, 55-62, (1936)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) fundamental group of an affine curve; characteristic \(p\); mock covers; \(p\)-group; finite group generated by \(p\)-subgroups; finite groups realized as Galois groups over affine curves; Monster; deformation of curves; branch points Merkurjev, A.S., Suslin, A.A.: \(K\)-cohomology of Severi-Brauer varieties and the norm residue homomorphism (in Russian). Izv. Akad. Nauk SSSR Ser. Mat. \textbf{46}, 1011-1046, 1135-1136 (1982). English translation: Math. USSR-Izv. \textbf{21}, 307-340 (1983)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Riemann surfaces; algebraic curves; automorphisms; fields of moduli Hidalgo, Rubén A., Non-hyperelliptic Riemann surfaces with real field of moduli but not definable over the reals, Arch. Math. (Basel), 93, 3, 219-224, (2009)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) plane algebraic curves; birational geometry of surfaces; affine automorphisms Blanc, J.; Stampfli, I.: Automorphisms of the plane preserving a curve. J. algebraic geom. 2, No. 2, 193-213 (2015)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) finite subgroups of rotation group; groups; linear algebra; infinite dimensional spaces; systems of linear differential equations; symmetry; free groups; generators; relations; Todd-Coxeter algorithm; bilinear forms; spectral theorems; linear groups; group representations; rings; algebraic geometry; factorization; modules; function fields and their relations to Riemann surfaces; Galois theory Artin, M.: Algebra. Prentice-Hall, Englewood Cliffs (1991)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) zeta functions; distribution of zeros; \(L\)-functions; finite fields; automorphic \(L\)-functions; GUE measure; Montgomery-Odlyzko law; normalized spacings; Wigner measure; Kolmogoroff-Smirnov discrepancy function; generalized Sato-Tate conjecture; low-lying zeros; \(L\)-functions of elliptic curves; spacings of eigenvalues; Haar measure; Fredholm determinants; Deligne's equidistribution theorem; monodromy; Kloosterman sums N.M. Katz and P. Sarnak. \textit{Random matrices, Frobenius eigenvalues, and monodromy, vol. 45 of American Mathematical Society Colloquium Publications}. American Mathematical Society, Providence, RI (1999).
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Tate pairing; discrete logarithm; elliptic curves; multiplicative group of finite fields Frey, G.; Müller, M.; Rüuck, H., The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems, IEEE Transactions on Information Theory, 45, 5, 1717-1719, (1999)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Picard group; \(SK_ 1\) of affine rings of plane cubic curves Krusemeyer M., Comm. in Alg 12 pp 65-- (1984)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic curves; étale coverings of the affine line; fundamental group; Drinfeld modular curves Joshi, K., A family of étale coverings of the affine line, J. number theory, 59, 414-418, (1996)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) classification up to isomorphism; elementary equivalence; function fields over algebraically closed fields; function fields of curves; elliptic curves D. Pierce , Function fields and elementary equivalence . Bull. London Math. Soc. 31 ( 1999 ), 431 - 440 . MR 1687564 | Zbl 0959.03022
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Mordell-Weil groups of elliptic curves with complex; multiplication; Weil parametrizations; L-function attached to a Weil curve; anti-cyclotomic tower; Iwasawa theory of elliptic curves; p-adic height pairing; p-adic L-functions; p-adic Heegner measures; finiteness of the Tate-Shafarevich group; Mordell-Weil groups of elliptic curves with complex multiplication B. Mazur, Modular curves and arithmetic, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 185 -- 211.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Kronecker's Jugendtraum; elliptic functions; elliptic integrals; arithmetic of elliptic curves; Weierstrass \(\wp\)-function; projective plane cubics; Abel's theorem; inversion problem; Jacobi functions; theta functions; Lefschetz theorem; embeddings; theta identities; Euler identities; Jacobi substitutions; quadratic reciprocity; Siegel modular group; modular forms; Eisenstein series; modular equation; arithmetic subgroups; arithmetic applications; solvability of algebraic equations; Galois theory; Klein's icosaeder; quintic equation; imaginary quadratic number fields; class invariants; class polynomial; Mordell-Weil theorem Henry McKean and Victor Moll, \textit{Elliptic Curves}, Cambridge University Press, Cambridge, 1997.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) group of polynomial automorphisms of a real compact affine variety M. W. Hirsch, Automorphisms of compact affine varieties, in Global Analysis in Modern Mathematics (Orono, ME, 1991; Walthom, MA, 1992), Publish or Perish, Houston, TX, 1993, pp. 227--245.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Iwasawa theory of totally real number fields; covering of algebraic curves over a finite field; Drinfel'd modules; Picard group; L-series David Goss, The theory of totally real function fields, Applications of algebraic \?-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 449 -- 477.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) function fields; finite fields; hyperelliptic curves; lower bounds for moments; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory Andrade, J. C.: Rudnick and soundararajan's theorem for function fields. Finite fields appl. 37, 311-327 (2016)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) central division algebras over the function field of a curve; Brauer group; elliptic curves V. I. Yanchevskiĭ and G. L. Margolin, Brauer groups of local hyperelliptic curves with good reduction, Algebra i Analiz 7 (1995), no. 6, 227 -- 249 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 7 (1996), no. 6, 1033 -- 1048. V. I. Yanchevskiĭ and G. L. Margolin, Erratum: ''Brauer groups of local hyperelliptic curves with good reduction'', Algebra i Analiz 8 (1996), no. 1, 237 (Russian).
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) moduli space of smooth curves; branch locus; isolated points; group of automorphisms Gómez González E. (1996) Irreductible components and isolated points in the branch locus of the moduli space of smooth curves. Bol. Soc. Mat. Mexicana 2(3): 115--128
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) p-adic analog of the Weierstrass sigma function; complex elliptic curves; formal group; canonical heights; characteristic p; p-adic theta functions Fontaine, J.-M.: Le corps des périodes \(p\)-adiques. With an appendix by Pierre Colmez. Périodes \(p\)-adiques (Bures-sur-Yvette, 1988). Astérisque No. 223, pp. 59-111 (1994)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic geometric codes; algebraic curves over finite fields; function fields; Goppa codes; complexity of multiplication in extension fields; divisors of curves of genus 1; weight distributions; minimal weight
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Hasse-Weil bound; maximal curve; geometric Goppa code; asymptotically good sequence; survey; number of rational points; curves over finite fields; towers of function fields van der Geer, G., Curves over finite fields and codes, (European congress of mathematics, vol. II, Barcelona, 2000, Prog. math., vol. 202, (2001), Birkhäuser Basel), 225-238
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) coverings of \(\mathbb{P}^ 1\); Galois groups; Hurwitz monodromy group; finite groups; Galois group of regular extension of \(\mathbb{Q}\); universal Frattini cover; rational point on varieties; regular realization problem on dihedral groups; real branch points; totally nonsplit extension; field of totally real numbers; fields of definition; inverse Galois problem; symmetric group; modular curves Dèbes, Pierre; Fried, Michael D., Nonrigid constructions in Galois theory, Pacific J. math., 163, 1, 81-122, (1994)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) modular function \(j(\tau)\); singular moduli; prime factorization of the absolute norm; modular polynomial; arithmetic of maximal orders in quaternion algebras; geometry of supersingular elliptic curves; Fourier coefficients; Eisenstein series; Hilbert modular group; local heights; Heegner points Gross, B. H.; Zagier, D. B., \textit{on singular moduli}, J. Reine Angew. Math., 355, 191-220, (1985)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) curves over a finite field; curves with many points; graphs; towers of function fields; zeta functions ] Emmanuel Hallouin and Marc Perret, From Hodge index theorem to the number of points of curves over finite fields, arXiv:1409.2357v1, 2014.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) genus of curves over finite fields; many rational points; maximal function fields R. Fuhrmann and F. Torres. The genus of curves over finite fields with many rational points. Manuscripta Math., 89(1) (1996), 103--106.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Pierre de Fermat; René Descartes; Leonhard Euler; affine space; barycenter; real affine space; Pasch's theorem; Euclidean space; metric space; Gram-Schmidt process; approximation by the law of least squares; Fourier approximation; Hermitian space; projective space; duality principle; Fano's theorem; projective quadric; Pascal's theorem; Brianchon's theorem; topology of projective real spaces; algebraic plane curves; Bezout's theorem; Hessian curve; Cramer's paradox; group of a cubic; rational algebraic plane curve; Taylor's formula for polynomials in one or more variables; Eisenstein's criterion; Euler's formula; fundamental theorem of algebra; Sylvester's theorem
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) stable reduction of curves; completely valued fields; ultrametric valuation; topological function field; topological genus; inequalities
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) non-vanishing of \(L\)-functions; twisted \(L\)-functions of elliptic curves; function fields; elliptic curve rank in extensions
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) moments of quadratic Dirichlet; \(L\)-functions; ratios of \(L\)-functions; function fields; random matrix theory; hyperelliptic curves Andrade, J. C.; Keating, J. P., Conjectures for the integral moments and ratios of \textit{L}-functions over function fields, J. Number Theory, 142, 102-148, (2014)
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) group of automorphisms of affine space; actions of finite dimensional algebraic groups; non-triangular actions of the additive group V. Popov, On actions of \(G_a\) on \(A^n\) , in Algebraic groups , \nLecture Notes in Math., 1271 (1986), 237-242.
0
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Brauer group of the rational function fields
0