In this paper we investigate the image of the $l$-adic representation attached to
the Tate module of an abelian variety defined over a number field. We consider
simple abelian varieties of type III in the Albert classification. We compute
the image of the $l$-adic and mod $l$ Galois representations and we prove the
Mumford-Tate and Lang conjectures for a wide class of simple abelian varieties
of type III.
Publié le : 2010-05-15
Classification:
$l$-adic representation,
abelian variety,
Lie algebra,
linear algebraic group,
14K15,
17B45
@article{1277298644,
author = {Banaszak, Grzegorz and Gajda, Wojciech and Kraso\'n, Piotr},
title = {On the image of Galois $l$-adic representations for abelian varieties of type III},
journal = {Tohoku Math. J. (2)},
volume = {62},
number = {1},
year = {2010},
pages = { 163-189},
language = {en},
url = {http://dml.mathdoc.fr/item/1277298644}
}
Banaszak, Grzegorz; Gajda, Wojciech; Krasoń, Piotr. On the image of Galois $l$-adic representations for abelian varieties of type III. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp. 163-189. http://gdmltest.u-ga.fr/item/1277298644/