Vol. 2, No. 1, 2008

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Construction de $(\varphi,\varGamma)$-modules: représentations p-adiques et B-paires

Laurent Berger

Vol. 2 (2008), No. 1, 91–120
Abstract

Soit Be = Bcrisφ=1. On étudie la catégorie des B-paires (We,WdR+)We est un Be-module libre muni d’une action semi-linéaire et continue de GK et où WdR+ est un BdR+-réseau stable par GK de BdR BeWe. Cette catégorie contient celle des représentations p-adiques, et est naturellement équivalente à la catégorie de tous les (φ,Γ)-modules sur l’anneau de Robba.

Let Be = Bcrisφ=1. We study the category of B-pairs (We,WdR+) where We is a free Be-module with a semilinear and continuous action of GK and where WdR+ is a GK-stable BdR+-lattice in BdR BeWe. This category contains the category of p-adic representations and is naturally equivalent to the category of all (φ,Γ)-modules over the Robba ring.

Keywords
$p$-adic Hodge theory, $(\varphi,\Gamma)$-modules, Frobenius slopes, $B$-pairs
Mathematical Subject Classification 2000
Primary: 11F80
Secondary: 14F30, 11S25, 11S20, 11S15, 11F85
Milestones
Received: 12 July 2007
Revised: 29 September 2007
Accepted: 29 September 2007
Published: 1 February 2008
Authors
Laurent Berger
UMPA ENS Lyon
46 allée d’Italie
69364 Lyon Cedex 07
France
http://www.umpa.ens-lyon.fr/~lberger