Let V be a p-adic representation of the absolute Galois group G of Qp that becomes crystalline over a finite tame extension, and assume p = 2. We provide necessary and sufficient conditions for V to be isomorphic to the p-adic Tate module Vp(A) of an abelian variety A defined over Qp. These conditions are stated on the filtered (ϕ, G)module attached to V .
This paper is devoted to the study of the l-adic representations of the absolute Galois group G of Q p , p 5, associated to an elliptic curve over Q p , as l runs through the set of all prime numbers (including l p, in which case we use the theory of potentially semi-stable p-adic representations).Brought to you by | University of Iowa Libraries Authenticated Download Date | 5/31/15 4:50 AM 2) Le Q p G-module V p E est potentiellement semi-stable et de type Hodge-Tate 0Y 1.
We show the existence of abelian surfaces A over Qp having good reduction with supersingular special fiber whose associated p-adic Galois module Vp(A) is not semisimple.
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