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 $J$. 
@article{IM2_1992_39_1_a7,
     author = {S. G. Tankeev},
     title = {Kuga--Satake abelian varieties and $l$-adic representations},
     journal = {Izvestiya. Mathematics },
     pages = {855--867},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_39_1_a7/}
}
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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/