On the $\ell$-adic Galois representations attached to nonsimple abelian varieties

Abstract

We study Galois representations attached to nonsimple abelian varieties over finitely generated fields of arbitrary characteristic. We give sufficient conditions for such representations to decompose as a product, and apply them to prove arithmetical analogues of results shown by Moonen and Zarhin in the context of complex abelian varieties (of dimension at most 5).

Final version, to appear in the Annales de l'Institut Fourier

References in corpus (1)

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

Cited by in corpus (2)

• Integral and adelic aspects of the Mumford-Tate conjecture
• A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties