Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups

2020/02/27 by WonTae Hwang, Hwang, WonTae, Kyunghwan Song +1
Computer Science · Mathematics · #11G25 #14K02 #20B25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Number Theory (math.NT) #Primary 11G10

paper · pdf · doi:10.48550/arxiv.2002.12353

openalex publication_date 2020/02/27 · openalex created_date 2020/03/06 · openalex updated_date 2026/07/28

Abstract

For each Sophie Germain prime g ≥ 5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is a cyclic group of order 4g+2. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.

Related

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