Geodesic
Endomorphisms of abelian varieties over fields of finite characteristic
Izvestiya. Mathematics , Tome 9 (1975) no. 2, pp. 255-260

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The semisimplicity of $l$-adic representations corresponding to one-dimensional étale cohomology, and a proof of the Tate's conjecture about homomorphisms of abelian varieties, are derived from the Tate's finiteness conjecture on isogenies of polarized abelian varieties. Bibliography: 4 items. 
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     author = {Yu. G. Zarhin},
     title = {Endomorphisms of abelian varieties over fields of finite characteristic},
     journal = {Izvestiya. Mathematics },
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     number = {2},
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Yu. G. Zarhin. Endomorphisms of abelian varieties over fields of finite characteristic. Izvestiya. Mathematics , Tome 9 (1975) no. 2, pp. 255-260. http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a2/