Quasi-semi-stable representations

Abstract : Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of p-adic torsion representations of G_\infty, named quasi-semi-stable. We prove that these representations are "explicitly" described by a certain category of linear algebra objects. The results of this note should be consider as a first step in the understanding of the structure of quotients of two lattices in a crystalline (resp. semi-stable) Galois representation.
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  • HAL Id : hal-00172014, version 2
  • ARXIV : 0709.2118

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Xavier Caruso, Tong Liu. Quasi-semi-stable representations. Bulletin de la société mathématique de France, 2009, 137 (2), pp.185-223. ⟨hal-00172014v2⟩

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