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

2019/01/12 by Hwang, WonTae
#11G10 #11G25 #14K02 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.04470

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.

Related

• Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups
• A classification of the automorphism groups of polarized abelian threefolds over finite fields
• On the automorphism groups of simple polarized abelian fourfolds over finite fields and Jordan constants
• On a classification of the automorphism groups of polarized abelian surfaces over finite fields
• Polarizations on abelian varieties