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arXiv · 2011.13708

Characteristic Polynomials of Simple Ordinary Abelian Varieties over Finite Fields

Lenny Jones
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Abstract

We provide an easy method for the construction of characteristic polynomials of simple ordinary abelian varieties ${\mathcal A}$ of dimension $g$ over a finite field ${\mathbb F}_q$, when $q\ge 4$ and $2g=\rho^{b-1}(\rho-1)$ for some prime $\rho\ge 5$, with $b\ge 1$. Moreover, we show that ${\mathcal A}$ is absolutely simple if $b=1$ and $\rho=5$, but ${\mathcal A}$ is not absolutely simple for arbitrary $\rho$ with $b>1$.

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Lenny Jones. 2020-11-27. Characteristic Polynomials of Simple Ordinary Abelian Varieties over Finite Fields. https://arxiv.org/abs/2011.13708

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