Weil polynomials of small degree

2025/05/30 by Stefano Marseglia, Marseglia, Stefano · 2 citations
Computer Science · Mathematics · #12D10 #14K15 #26C10 #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.2505.24546

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Honda and Tate showed that the isogeny classes of abelian varieties of dimension g over a finite field \mathbbF_q are classified in terms of q-Weil polynomials of degree 2g, that is, monic integer polynomials whose set of complex roots consists of g conjugate pairs of absolute value √(q). There are descriptions of the space of such polynomials for g ≤ 5, but for g=3, 4 and 5, these results contain mistakes. We correct these statements. Our proofs build on a criterion that determines when a real polynomial has only real roots in terms of the non-necessarily distinct roots of its first derivative.

Cited by

• On Weil Polynomials of Hyperelliptic Curves over Finite Fields of Characteristic 2
• Maximal Curves With Respect To Quadratic Extensions Over Finite Fields

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