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

Xavier Caruso (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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. Under a technical hypothesis, 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.

Mots clés: représentations galoisiennes p-adiques; représentations semi-stables

Domaines: Théorie des nombres [math.NT]

Xavier Caruso. Représentations galoisiennes p-adiques et (phi,tau)-modules. 2010. ⟨hal-00528714v1⟩