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Structures de Hodge–Pink pour les φ/𝔖-modules de Breuil et Kisin

Part of: Algebraic groups Algebraic number theory: local and $p$-adic fields (Co)homology theory

Published online by Cambridge University Press:  03 May 2012

Alain Genestier  and
Vincent Lafforgue
Alain Genestier
Affiliation:
Institut Élie Cartan, Université Henri Poincaré-Nancy 1, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy cedex, France (email: alain.genestier@iecn.u-nancy.fr)
Vincent Lafforgue
Affiliation:
CNRS, MAPMO - Université d’Orléans, Bâtiment de mathématiques, Rue de Chartres, B.P. 6759, F-45067 Orléans cedex 2, France (email: vlafforg@math.jussieu.fr)
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Abstract

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In this article, we apply the methods of our work on Fontaine’s theory in equal characteristics to the φ/𝔖-modules of Breuil and Kisin. Thanks to a previous article of Kisin, this yields a new and rather elementary proof of the theorem ‘weakly admissible implies admissible’ of Colmez and Fontaine.

Résumé

Dans cet article, nous appliquons les méthodes de notre travail sur la théorie de Fontaine en égales caractéristiques aux φ/𝔖-modules de Breuil et Kisin. Grâce à un article précédent de Kisin, cela fournit une nouvelle démonstration assez élémentaire du théorème ‘faiblement admissible implique admissible’ de Colmez et Fontaine.

Keywords

Fontaine theoryBreuil–Kisin modulesDieudonné modulesHodge structures

MSC classification

Secondary: 11S20: Galois theory 14F30: $p$-adic cohomology, crystalline cohomology 14L05: Formal groups, $p$-divisible groups
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 751 - 789
Copyright
Copyright © Foundation Compositio Mathematica 2012

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