In this note we give a complete proof of Theorem 4.1 of , 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|
|Number of pages||18|
|Journal||Journal de Theorie des Nombres de Bordeaux|
|State||Published - 2010|
ASJC Scopus subject areas
- Algebra and Number Theory