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.
"On the image of Galois $l$-adic representations for abelian varieties of type III." Tohoku Math. J. (2) 62 (2) 163 - 189, 2010. https://doi.org/10.2748/tmj/1277298644