Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras

TL;DR

This paper proves an analogue of the Tate conjecture concerning homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.

Contribution

It establishes a new result extending the Tate conjecture to a broader class of fields and abelian varieties.

Findings

Proves Tate conjecture analogue for infinite cyclotomic extensions

Extends understanding of homomorphisms of abelian varieties

Links Lie algebras to abelian variety endomorphisms

Abstract

We prove an analogue of the Tate conjecture on homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.