%0 Journal Article %T Homomorphisms of abelian varieties over geometric fields of finite characteristic %A Yuri G. Zarhin %J Mathematics %D 2010 %I arXiv %X We study analogues of Tate's conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of abelian varieties without nontrivial endomorphisms. %U http://arxiv.org/abs/1012.5083v3