Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T19:03:49.494Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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