Geodesic
Minimal models of curves of genus~2 and homomorphisms of abelian varieties defined over a~field of finite characteristic
Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 65-108

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In this article, we prove a finiteness theorem for isogenous abelian varieties of dimension 2 defined over a field of algebraic functions of one variable whose characteristic $\ne2$. By means of this result, we prove Tate's conjecture on homomorphisms of abelian varieties of dimension 1 defined over the same field. 
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     author = {A. N. Parshin},
     title = {Minimal models of curves of genus~2 and homomorphisms of abelian varieties defined over a~field of finite characteristic},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a2/}
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A. N. Parshin. Minimal models of curves of genus~2 and homomorphisms of abelian varieties defined over a~field of finite characteristic. Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 65-108. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a2/