Geodesic
On~algebraic cycles on surfaces and Abelian varieties
Izvestiya. Mathematics , Tome 18 (1982) no. 2, pp. 349-380

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This paper contains a proof of the Tate conjecture on algebraic cycles on surfaces with strongly degenerate reduction over function fields and the Hodge conjecture on cycles on simple Abelian varieties of the first and second types according to Albert's classification (under certain restrictions on the dimension of the variety and the center of its ring of endomorphisms). Bibliography: 27 titles. 
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     author = {S. G. Tankeev},
     title = {On~algebraic cycles on surfaces and {Abelian} varieties},
     journal = {Izvestiya. Mathematics },
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S. G. Tankeev. On~algebraic cycles on surfaces and Abelian varieties. Izvestiya. Mathematics , Tome 18 (1982) no. 2, pp. 349-380. http://geodesic.mathdoc.fr/item/IM2_1982_18_2_a4/