#### DOCUMENTA MATHEMATICA,
Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 35-75

** G. Banaszak, W. Gajda, P. Krason **
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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