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

Banaszak, Grzegorz; Gajda, Wojciech; Krason, Piotr

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

Authors

Banaszak, Grzegorz

Gajda, Wojciech

Krason, Piotr

Description

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.
34 pages