Banaszak, G.; Gajda, W.; Krasoń, P.

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

Doc. Math. (Bielefeld) Extra Vol. John H. Coates' Sixtieth Birthday, 35-75 (2006)

Summary

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.

Mathematics Subject Classification

11F80, 11G10

Keywords/Phrases

abelian varieties, $l$-adic representations

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