On the image of l-adic Galois representations for abelian varieties of type I and II

Details On the image of l-adic Galois representations for abelian varieties of type I and II On the image of l-adic Galois representations for abelian varieties of type I and II

2004-07-14

arxiv.org/abs/math/0407247v1

Mathematics

Number Theory

34 pages

Scientific paper

In this paper we investigate the image of the $l$-adic representation attached to the Tate module of an abelian variety over a number field with endomorphism algebra of type I or II in the Albert classification. We compute the image explicitly and verify the classical conjectures of Mumford-Tate, Hodge, Lang and Tate, for a large family of abelian varieties of type I and II. In addition, for this family, we prove an analogue of the open image theorem of Serre.

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