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arXiv · 2506.13706

Weil polynomials of abelian varieties over finite fields

Michael Cerchia·Zeyu Liu·Diana Mocanu·Haodong Yao·Jing Ye
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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.

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Michael Cerchia, Zeyu Liu, Diana Mocanu, Haodong Yao, Jing Ye. 2025-06-16. Weil polynomials of abelian varieties over finite fields. https://arxiv.org/abs/2506.13706

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