Interrelations between the Tate and Hodge conjectures for Abelian varieties

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.