Modules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields

arXiv2208.05409MaRDI QIDQ6407519

Stefano Marseglia

Publication date: 10 August 2022

Abstract: We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an algorithm to compute the $mathbb{F}_q$-isomorphism classes of abelian varieties over a finite field $mathbb{F}_q$ which belong to an isogeny class determined by a characteristic polynomial $h$ of Frobenius when $h$ is ordinary, or $q$ is prime and $h$ has no real roots.

Has companion code repository: https://github.com/stmar89/alget

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Arithmetic ground fields for abelian varieties (14K15) Matrices of integers (15B36) Lattices over orders (16H20)

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