Geodesic
On the image of $l$-adic Galois representations for abelian varieties of type I and II
Documenta mathematica, John H. Coates' Sixtieth Birthday (2006), pp. 35-75.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11F80, 11G10
Keywords: abelian varieties, $l$-adic representations 
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     author = {Banaszak, G. and Gajda, W. and Kraso\'n, P.},
     title = {On the image of $l$-adic {Galois} representations for abelian varieties of type {I} and {II}},
     journal = {Documenta mathematica},
     pages = {35--75},
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     volume = {John H. Coates' Sixtieth Birthday},
     year = {2006},
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Banaszak, G.; Gajda, W.; Krasoń, P. On the image of $l$-adic Galois representations for abelian varieties of type I and II. Documenta mathematica, John H. Coates' Sixtieth Birthday (2006), pp. 35-75. http://geodesic.mathdoc.fr/item/DOCMA_2006__S5__a22/