Geodesic
Abelian varieties and the general Hodge conjecture
Izvestiya. Mathematics , Tome 43 (1994) no. 1, pp. 179-191.

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The Grothendieck version of the general Hodge conjecture is proved for certain simple complex abelian varieties of the $1^{\operatorname{st}}$ type with regard to Albert's classification and for certain abelian varieties of CM-type. 
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S. G. Tankeev. Abelian varieties and the general Hodge conjecture. Izvestiya. Mathematics , Tome 43 (1994) no. 1, pp. 179-191. http://geodesic.mathdoc.fr/item/IM2_1994_43_1_a10/

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