On the Image of l-Adic Galois Representations for Abelian Varieties of Type I and II

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.

2000 Mathematics Subject Classification: 11F80, 11G10

Keywords and Phrases: abelian varieties, l-adic representations

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