Poids de l’inertie modérée de certaines représentations cristallines

Translated title of the contribution: Tame inertia weights of certain crystalline representations

Xavier Caruso, David L Savitt

Research output: Contribution to journalArticle

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.

Original languageFrench
Pages (from-to)79-96
Number of pages18
JournalJournal de Theorie des Nombres de Bordeaux
Volume22
Issue number1
DOIs
StatePublished - 2010

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Inertia
P-adic Fields
Galois group
Interval
Theorem
Family

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Poids de l’inertie modérée de certaines représentations cristallines. / Caruso, Xavier; Savitt, David L.

In: Journal de Theorie des Nombres de Bordeaux, Vol. 22, No. 1, 2010, p. 79-96.

Research output: Contribution to journalArticle

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