Abstract
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 semisimplification 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.
Translated title of the contribution | Tame inertia weights of certain crystalline representations |
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Original language | French |
Pages (from-to) | 79-96 |
Number of pages | 18 |
Journal | Journal de Theorie des Nombres de Bordeaux |
Volume | 22 |
Issue number | 1 |
DOIs | |
State | Published - 2010 |
Externally published | Yes |
ASJC Scopus subject areas
- Algebra and Number Theory