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Tohoku Mathematical Journal
SECOND SERIES VOL. 62, NO. 2
|Tohoku Math. J.|
62 (2010), 163-189
ON THE IMAGE OF GALOIS $l$-ADIC REPRESENTATIONS FOR ABELIAN VARIETIES OF TYPE III
Grzegorz Banaszak, Wojciech Gajda and Piotr Krasoń
(Received September 16, 2008, revised December 1, 2009)
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.
2000 Mathematics Subject Classification.
Primary 14K15; Secondary 17B45.
Key words and phrases.
$l$-adic representation, abelian variety, Lie algebra, linear algebraic group.
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