On a classification of the automorphism groups of polarized abelian surfaces over finite fields

TL;DR

This paper classifies the largest possible automorphism groups of polarized abelian surfaces over finite fields, providing a comprehensive understanding of their symmetry structures.

Contribution

It offers a complete classification of maximal automorphism groups for polarized abelian surfaces over finite fields, a previously unresolved problem.

Findings

Identified all maximal automorphism groups for polarized abelian surfaces over finite fields.

Established criteria for when a finite group can be realized as such an automorphism group.

Provided a framework for understanding symmetry in abelian surfaces over finite fields.

Abstract

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.