Weil polynomials of abelian varieties over finite fields

TL;DR

This paper studies Weil polynomials associated with abelian varieties over finite fields, providing necessary conditions and explicit criteria for their occurrence as characteristic polynomials of Frobenius endomorphisms.

Contribution

It introduces new necessary conditions and explicit criteria for identifying Weil polynomials of specific degrees related to abelian varieties over finite fields.

Findings

Necessary condition for degree 12 Weil polynomials.

Explicit criteria for degree 14 Weil polynomials.

Characterization of Frobenius characteristic polynomials.

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.