Tate Conjecture And Finiteness of Abelian Varieties over Finite Field

2018/08/14 by Gao, Anningzhe
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.04783

Abstract

In this paper we will prove that Tate conjecture of abelian varieties over finite field is equivalent to the finiteness of isomorphism classes of abelian varieties with a fixed dimension. We give a different approach with Zarhin's result.

Related

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• Homomorphisms of abelian varieties over geometric fields of finite characteristic
• On the Tate and Standard Conjectures over Finite Fields
• The Tate conjecture over finite fields (AIM talk)
• Note on the counterexamples for the integral Tate conjecture over finite fields