Geodesic
Kuga--Satake abelian varieties and $l$-adic representations
Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 855-867.

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Let $J$ be a Kuga–Satake abelian variety defined over a number field $k\hookrightarrow\mathbf C$. Assuming a certain arithmetic condition on the canonical field $K$ associated to $J\otimes_k\mathbf C$, we prove the Mumford–Tate conjecture concerning the Lie algebra of the image of the $l$-adic representation in the one-dimensional cohomology of $J$. 
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S. G. Tankeev. Kuga--Satake abelian varieties and $l$-adic representations. Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 855-867. http://geodesic.mathdoc.fr/item/IM2_1992_39_1_a7/

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