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

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

2003-05-22

arxiv.org/abs/math/0305314v2

Mathematics

Number Theory

28 pages

Scientific paper

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 (\phi,G)-module attached to V.

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