Geodesic
A~remark on endomorphisms of abelian varieties over function fields of finite characteristic
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 477-480

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Assuming Tate's finiteness conjecture, we prove some consequences of Tate's conjecture on homomorphisms of abelian varieties. 
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     author = {Yu. G. Zarhin},
     title = {A~remark on endomorphisms of abelian varieties over function fields of finite characteristic},
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Yu. G. Zarhin. A~remark on endomorphisms of abelian varieties over function fields of finite characteristic. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 477-480. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a1/