# Automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields

## TL;DR

This paper proves that automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic and provides a complete classification of possible automorphism groups.

## Contribution

It establishes the cyclic nature of these automorphism groups and offers a comprehensive list of all finite groups that can occur as such automorphism groups.

## Key findings

- Automorphism groups are cyclic for the specified varieties.
- Complete classification of possible automorphism groups.
- Identification of all realizable finite groups.

## Abstract

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.