Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures)
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.
Faisceaux pervers, transformation de Mellin et déterminants
Fake CM and the stable model of .
Faltings modular height and self-intersection of dualizing sheaf.
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.
Families of Mumford curves
Fibres vectoriels homogenes sur les varietes abeliennes qui sont des tores analytiques (rigides).
Fibrés vectoriels semi-stables sur une courbe de Mumford.
Fields of definition for some Hodge cycles.
Fields of definition of algebraic varieties in characteristic zero
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,...
Filtration par le poids sur la cohomologie de de Rham d'une courbe projective non singulière sur un corps ultramétrique complet
Finding the eigenvalue in Elkies' algorithm.
Finite locally free group schemes in characteristic p and Dieudonné modules.
Finite projective planes, Fermat curves, and Gaussian periods
One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences involving...
Finiteness theorems for torsion of abelian varieties over large algebraic fields
Flèches de spécialisations en cohomologie étale et applications arithmétiques
Fonction de Seshadri arithmétique en géométrie d’Arakelov
To any adelic invertible sheaf on a projective arithmetic variety and any regular algebraic point of the arithmetic variety, we associate a function defined on which measures the separation of jets on this algebraic point by the “small” sections of the adelic invertible sheaf. This function will be used to study the arithmetic local positivity.