Représentations p-adiques et normes universelles, I. Le cas cristallin
Bernadette Perrin-Riou
Abstract
Let V be a crystalline p-adic representation of the absolute Galois group GK of an finite unramified extension K of Qp and T a lattice of V stable by GK. We prove the following result: Let Fil1 V be the maximal sub-representation of V with Hodge-Tate weights strictly positive and Fil1 T=T Fil1 V. Then, the projective limit of the H1g(K(μpn), T) is equal up to torsion to the projective limit of the H1(K(μpn), Fil1 T). So its rank over the Iwasawa algebra is [K:Qp] dim Fil1 V.
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