Fonctions L en géométrie rigide I: F-modules convergents ou surconvergents et conjecture de Dwork - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2009

Fonctions L en géométrie rigide I: F-modules convergents ou surconvergents et conjecture de Dwork

Abstract

This article is the first one of a series of three articles devoted to L-functions. In this one we give a definition of the L-functions of convergent or overconvergent F- modules with the help of Teichmüller liftings and we establish the meromorphy of the L-functions of convergent F- modules in the closed unit disk. Whereas Wan established Dwork conjecture in a series of three articles , we give here a proof relying only on the generalyzed Monsky's trace formula of Wan and on an isogeny theorem of Katz. In the second article we'll give a definition of the L-functions of F-(iso)crystals by cohomological means and we'll show how it matches with the one given here: it gives back the one used in crystalline cohomology by Katz or Etesse, or the one used in rigid cohomology by Etesse-Le Stum, or the one used by Wan ; the aim is then to give a proof of Katz conjecture on p-adic unit roots and poles of these L-functions using rigid cohomology. In the third article we give an explicit form of these results for ordinary abelian schemes.
Fichier principal
Vignette du fichier
FonctionsLengeometrierigideI.pdf (308.85 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00425929 , version 1 (22-10-2009)
hal-00425929 , version 2 (21-01-2010)
hal-00425929 , version 3 (07-02-2010)
hal-00425929 , version 4 (16-12-2010)

Identifiers

Cite

Jean-Yves Etesse. Fonctions L en géométrie rigide I: F-modules convergents ou surconvergents et conjecture de Dwork. 2009. ⟨hal-00425929v3⟩

Collections

IRMAR-GA
126 View
80 Download

Altmetric

Share

Gmail Facebook X LinkedIn More