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

Grzegorz Banaszak·Wojciech Gajda·Piotr Krason
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Abstract

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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Grzegorz Banaszak, Wojciech Gajda, Piotr Krason. 2004-07-14. On the image of l-adic Galois representations for abelian varieties of type I and II. https://arxiv.org/abs/math/0407247

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