Homomorphisms of abelian varieties over geometric fields of finite characteristic

TL;DR

This paper investigates analogues of Tate's conjecture concerning homomorphisms of abelian varieties over certain geometric fields, focusing on cases without nontrivial endomorphisms, advancing understanding in algebraic geometry.

Contribution

It extends Tate's conjecture to abelian varieties over finitely generated fields over algebraic closures of finite fields, specifically addressing the case with trivial endomorphisms.

Findings

Results cover abelian varieties without nontrivial endomorphisms.

Provides new insights into homomorphism structures over geometric fields.

Advances the understanding of Tate's conjecture in positive characteristic.

Abstract

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.