Facteurs -simples de de grande dimension et de grand rang
Factoring polynomials in finite fields: an application of Lang-Weil to a problem in graph theory.
Factorization estimates for abelian varieties
Failure of the Hasse principle for Châtelet surfaces in characteristic
Given any global field of characteristic , we construct a Châtelet surface over that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic , thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
Fake CM and the stable model of .
Families of elliptic curves of high rank with nontrivial torsion group over ℚ
Families of hypersurfaces of large degree
Grauert and Manin showed that a non-isotrivial family of compact complex hyperbolic curves has finitely many sections. We consider a generic moving enough family of high enough degree hypersurfaces in a complex projective space. We show the existence of a strict closed subset of its total space that contains the image of all its sections.
Familles de polynômes liées aux courbes modulaires X₁(l) unicursales et points rationnels non-triviaux de courbes elliptiques quotient
Familles de revêtements de la droite projective
Fibrations of low genus, I
Field of moduli versus field of definition for cyclic covers of the projective line
We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli that can not be defined over is also given.
Fields of definition of building blocks with quaternionic multiplication
Fields of definition of -curves
Let be a -curve with no complex multiplication. In this note we characterize the number fields such that there is a curve isogenous to having all the isogenies between its Galois conjugates defined over , and also the curves isogenous to defined over a number field such that the abelian variety Res obtained by restriction of scalars is a product of abelian varieties of GL-type.
Fields of moduli of three-point -covers with cyclic -Sylow, II
We continue the examination of the stable reduction and fields of moduli of -Galois covers of the projective line over a complete discrete valuation field of mixed characteristic , where has a cyclic-Sylow subgroup of order . Suppose further that the normalizer of acts on via an involution. Under mild assumptions, if is a three-point -Galois cover defined over , then the th higher ramification groups above for the upper numbering of the (Galois closure of the) extension vanish,...
Finding the eigenvalue in Elkies' algorithm.
Finite automata and arithmetic.
Finiteness theorems for torsion of abelian varieties over large algebraic fields
Flèches de spécialisations en cohomologie étale et applications arithmétiques
Fonction zêta d’Epstein et dilogarithme de Bloch-Wigner
Nous exprimons certaines séries d’Epstein normalisées en comme combinaisons linéaires de dilogarithmes de Bloch-Wigner en des nombres algébriques des corps pour les discriminants associés à la forme quadratique.
Fonction zêta des hauteurs associée à une certaine surface cubique
L’objet de cet article est d’obtenir une formule pour la fonction zêta des hauteurs classique à partir de la fonction zêta des hauteurs multiple de La Bretèche, et d’utiliser cette formule pour prolonger de manière méromorphe la fonction zêta des hauteurs. En particulier, il est montré que celle-ci peut être prolongée au demi-plan et que la frontière naturelle de son domaine naturel de méromorphie est .