Geodesic
Interrelations between the Tate and Hodge conjectures for Abelian varieties
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 615-624

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In the paper the action of the Galois group $G(\overline k\mid k)$ on $H_l^m(A)$ is investigated, where $A$ is an Abelian variety defined over a field $k$ of characteristic zero. We prove that the Galois group acts on the rational cohomology classes of type $(p,p)$ as far as they are algebraic. Bibliography: 10 titles. 
@article{SM_1971_14_4_a9,
     author = {I. I. Pyatetskii-Shapiro},
     title = {Interrelations between the {Tate} and {Hodge} conjectures for {Abelian} varieties},
     journal = {Sbornik. Mathematics},
     pages = {615--624},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_4_a9/}
}
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I. I. Pyatetskii-Shapiro. Interrelations between the Tate and Hodge conjectures for Abelian varieties. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 615-624. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a9/