2018/05/31 by Stefano Marseglia
Computer Science · Mathematics · #Abelian group #Abelian variety #Algebraic Geometry and Number Theory #Automorphism #Coding theory and cryptography #Combinatorics #Crystallography #Discrete mathematics #Eigenvalues and eigenvectors #Elementary abelian group #Finite Group Theory Research #Finite field #Geometry #Isomorphism (crystallography) #Mathematics #Physics #Prime (order theory) #Pure mathematics #Quantum mechanics #Rank of an abelian group #Square (algebra) #Square matrix #Symmetric matrix #math.AG #math.NT #msc:11G10 #msc:11G25 #msc:14-04 #msc:14G15 #msc:14K15
paper · pdf · doi:10.1090/mcom/3594
published as Mathematics of Computation 90 (2021), no. 328, 953-971 · accepted by Math. Comp. major revision: added computation of the group of points; examples have been exported on the repo
arxiv created 2020/08/17 · openalex publication_date 2020/09/02 · arxiv updated 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field \mathbb Fq whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field \mathbb Fp whose characteristic polynomial is square-free and does not have real roots. In the ordinary case we are also able to compute the polarizations and the group of automorphisms (of the polarized variety) and, when the polarization is principal, the period matrix.