Primitive automorphisms of a simple abelian variety

TL;DR

This paper establishes that automorphisms of simple abelian varieties are primitive precisely when they have infinite order, providing a clear criterion for primitivity in this mathematical context.

Contribution

The paper proves a characterization of primitive automorphisms of simple abelian varieties based on their order, clarifying the structure of such automorphisms.

Findings

Automorphisms are primitive iff of infinite order.

Provides a necessary and sufficient condition for primitivity.

Enhances understanding of automorphism structure in abelian varieties.

Abstract

We shall prove that an automorphism of a simple abelian variety is primitive if and only if it is of infinite order.