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

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.

34 pages

References in corpus (1)

• Surjectivity Criteria for p-adic Representations, Part I

Cited by in corpus (5)

• On the $\ell$-adic Galois representations attached to nonsimple abelian varieties
• Torsion for abelian varieties of type III
• Finite group subschemes of abelian varieties over finite fields
• Explicit surjectivity of Galois representations attached to abelian surfaces and ${\mathrm{GL}}_2$-varieties
• Cycles in the de Rham cohomology of abelian varieties over number fields