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arXiv · 1602.07510

On the parity of supersingular Weil polynomials

David Ayotte·Antonio Lei·Jean-Christophe Rondy-Turcotte
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Abstract

Let q be an odd power of a prime p and let A/Fq be a supersingular abelian variety of dimension g. We show that if p>2g+1, then the characteristic polynomial of the q-Frobenius is an even polynomial. This generalizes the well-known result on the vanishing of the trace of the p-Frobenius when p>3 for supersingular elliptic curves over Fp.

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David Ayotte, Antonio Lei, Jean-Christophe Rondy-Turcotte. 2016-02-24. On the parity of supersingular Weil polynomials. https://doi.org/10.1007/s00013-016-0888-0

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