A classification of the automorphism groups of polarized abelian threefolds over finite fields

TL;DR

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

Contribution

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

Findings

Identified all maximal automorphism groups for the given class.

Established criteria for realizability of these groups.

Enhanced understanding of symmetry in algebraic geometry over finite fields.

Abstract

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