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arXiv · 1904.12173

Proportion of ordinarity in some families of curves over finite fields

Soumya Sankar
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Abstract

A curve over a field of characteristic $p$ is called ordinary if the $p$-torsion of its Jacobian as large as possible, that is, an $\mathbb{F}_p$ vector space of dimension equal to its genus. In this paper we consider the following question: fix a finite field $\mathbb{F}_q$ and a family $\mathscr{F}$ of curves over $\mathbb{F}_q$. Then, what is the probability that a curve in this family is ordinary? We answer this question when $\mathscr{F}$ is either the Artin-Schreier family in any characteristic or a superelliptic family in characteristic 2.

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Soumya Sankar. 2019-04-27. Proportion of ordinarity in some families of curves over finite fields. https://arxiv.org/abs/1904.12173

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