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Limites de représentations cristallines

Published online by Cambridge University Press:  15 October 2004

Laurent Berger
Laurent Berger
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138-2901, USAlaurent@math.harvard.edu
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Abstract

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Let F be the fraction field of the ring of Witt vectors over a perfect field of characteristic p (for example $F=\mathbb{Q}_p$), and let GF be the absolute Galois group of F. The main result of this article is the following: a p-adic representation of GF, which is a limit of subquotients of crystalline representations with Hodge–Tate weights in an interval [a; b], is itself crystalline with Hodge–Tate weights in [a; b]. In order to show this, we study the $(\phi,\Gamma)$-modules attached to crystalline representations, which allows us to improve some results of Fontaine, Wach and Colmez.

Keywords

p-adic representationscrystalline representationsWach modulesdeformations11F8011R2311S2512H2513K0514F30
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1473 - 1498
Copyright
Foundation Compositio Mathematica 2004