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Hodge and Newton and tame inertia polygons of semi-stable representations. (Polygones de Hodge, de Newton et de l’inertie modérée des représentations semi-stables.) (French) Zbl 1248.11092
Summary: 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 \(G_\infty\subset G_K\) its absolute Galois group. In this article, we define a class of \(p\)-adic torsion representations of \(G_\infty\), 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.

MSC:
11S15 Ramification and extension theory
14F30 \(p\)-adic cohomology, crystalline cohomology
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