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Représentations Cristallines et $F$-Cristaux: le Cas d'un Corps Résiduel Imparfait
Soit K un corps de valuation discrete complet, de caracteristique 0, a corps residuel k de caracteristique p. On note OK l’anneau de ses entiers. Soient $ une uniformisante de K, K une clotureExpand
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Image directe superieure et unipotence
Let X be a proper smooth curve over a perfect field of characteristic p > 0 and U an open dense subscheme of X . We prove that convergent F -isocrystals on U are overconvergent under the conditionExpand
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Log-cristaux et surconvergence
Nous montrons comment on peut construire en toute generalite un F-isocristal surconvergent a partir d'un F-log-cristal sur un log-schema au-dessus du point trivial. Nous etudions ensuite lesExpand
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Arithmetic Geometry over Global Function Fields
Cohomological Theory of Crystals over Function Fields and Applications.- On Geometric Iwasawa Theory and Special Values of Zeta Functions.- The Ongoing Binomial Revolution.- Arithmetic of Gamma, ZetaExpand
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On the non commutative Iwasawa main conjecture for abelian varieties over function fields
We establish the Iwasawa main conjecture for semi-stable abelian varieties over a function field of characteristic $p$ under certain restrictive assumptions. Namely we consider $p$-torsion freeExpand
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On the Selmer groups of abelian varieties over function fields of characteristic p > 0
Abstract We study a (p-adic) geometric analogue for abelian varieties over a function field of characteristic p of the cyclotomic Iwasawa theory and the non-commutative Iwasawa theory for abelianExpand
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Pontryagin duality for Iwasawa modules and abelian varieties
We prove a functional equation for two projective systems of finite abelian p-groups, {an} and {bn}, endowed with an action of Z d such that an can be identified with the Pontryagin dual of bn forExpand
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Parity conjectures for elliptic curves over global fields of positive characteristic
Abstract We prove the p-parity conjecture for elliptic curves over global fields of characteristic p>3. We also present partial results on the ℓ-parity conjecture for primes ℓ≠p.
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Fonction L unité d'un groupe de Barsotti-Tate
Abstract:The purpose of this article is to give a cohomological formula for the unit-root part of the L-function associated to a Barsotti-Tate group G on a scheme S over a field of characteristic pExpand
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