Représentations galoisiennes p-adiques et (phi,tau)-modules

Details Représentations galoisiennes p-adiques et (phi,tau)-modules Représentations galoisiennes p-adiques et (phi,tau)-modules

2010-10-23

arxiv.org/abs/1010.4846v2

Mathematics

Number Theory

45 pages

Scientific paper

Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the Breuil-Kisin extension K_infty. As a result, we obtain a new classification of p-adic representations of G_K = Gal(Kbar/K) by some (phi,tau)-modules. We then caracterize the (phi,tau)-modules, that correspond to semi-stable representations. As a corollary, we prove that every representation of G_K of E(u)-finite height is potentially semi-stable. It answers a question of Tong Liu. We finally describe a new classification of lattices is semi-stable representations in terms of recent Kisin theory.

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