Weil polynomials of abelian varieties over finite fields

2025/06/16 by Michael Cerchia, Zeyu Liu, Cerchia, Michael +7
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.13706

openalex publication_date 2025/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate Weil polynomials and their relationship with isogeny classes of abelian varieties over finite fields. We give a necessary condition for a degree 12 polynomial with integer coefficients to be a Weil polynomial. Moreover, we provide explicit criteria that determine when a Weil polynomial of degree 14 occurs as the characteristic polynomial of a Frobenius endomorphism acting on an abelian variety.

Citations

• The characteristic polynomials of abelian varieties of dimensions 3 over finite fields

Related

• Weil polynomials of abelian varieties over finite fields with many rational points
• Weil polynomials of small degree
• Deducing information about curves over finite fields from their Weil polynomials
• Cyclic abelian varieties over finite fields in ordinary isogeny classes
• Some arithmetic properties of Weil polynomials of the form t^2g+at^g+q^g