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A class of p-adic Galois representations arising from abelian varierties over Q_p

M. Volkov
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Abstract

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A) of an abelian variety A defined over Q_p. These conditions are stated on the filtered (ϕ,G)-module attached to V.

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M. Volkov. 2003-05-26. A class of p-adic Galois representations arising from abelian varierties over Q_p. https://arxiv.org/abs/math/0305314

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