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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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##### References:
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