On the computation of endomorphism rings of abelian surfaces over finite fields

2025/03/11 by Samuele Anni, Gaetan Bisson, Anni, Samuele +7
Computer Science · #11G07 #11G10 #11G15 #14H52 #14K02 #14K05 #14K10 #14K22 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.08925

openalex publication_date 2025/03/11 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each possible surface type, we survey known results and, whenever possible, provide improvements and missing results.

Related

• Computing the endomorphism ring of an ordinary abelian surface over a\n finite field
• Computing endomorphism rings of abelian varieties of dimension two
• Abelian surfaces admitting an (l,l)-endomorphism
• Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
• Abelian varieties over finite fields as basic abelian varieties