Représentations quasi-semi-stables

Abstract

Fix K a P-adic field and denote by Gk its absolute Galois group. Let k∞ be the extension of K obtained by adding Pn-th roots of a fixed uniformizer, and G∞ ⊂ Gk its absolute Galois group. In this article, we define a class of P-adic torsion representations of G∞ called quasi-semi-stable. We prove that these representations are "explicitly" described by a certain category of linear algebraic objects. The results of this note should be considered as a first step in the understanding of the structure of quotient of two lattices in a crystalline (resp. semi-stable) Galois representation. © SMF.