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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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/

[1] Zarkhin Yu. G., “Izogenii abelevykh mnogoobrazii nad polyami konechnoi kharakteristiki”, Matem. sb., 95:3 (1974), 461–470 | Zbl

[2] Parshin A. N., “Minimalnye modeli v krivykh roda 2 i gomomorfizmy abelevykh mnogoobrazii, opredelennykh nad polem konechnoi kharakteristiki”, Izv. AN SSSR. Ser. matem., 36 (1973), 67–109

[3] Tate J., “Algebraic cycles and poles of zeta functions”, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963), Harper Row,, New York, 1965, 93–110 | MR

[4] Tate J., “Endomorphisms of abelian varieties over finite fields”, Inv. Math., 2 (1966), 134–144 | DOI | MR | Zbl