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Xavier Caruso; David Savitt
Poids de l’inertie modérée de certaines représentations cristallines
Journal de théorie des nombres de Bordeaux, 22 no. 1 (2010), p. 79-96, doi: 10.5802/jtnb.705
Article PDF | Reviews MR 2675874 | Zbl 1223.14022

Résumé - Abstract

Tame inertia weights of certain crystalline representations

In this note we give a complete proof of Theorem 4.1 of [5], whose aim is to describe the action of tame inertia on the semi-simplification mod $p$ of a certain (small) family of crystalline representations $V$ of the absolute Galois group of a $p$-adic field $K$. This kind of computation was already accomplished by Fontaine and Laffaille when $K$ is absolutely unramified; in that setting, they proved that the action of tame inertia is completely determined by the Hodge-Tate weights of $V$, provided that those weights all belong to an interval of length $p-2$. The examples considered in this article show in particular that the result of Fontaine-Laffaille is no longer true when $K$ is absolutely ramified.

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