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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71888In 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 pagesNumber TheoryAlgebraic Geometry11G10; 14L15; 11R32On the image of l-adic Galois representations for abelian varieties of type I and IItext