A Mass Formula For Artin--Schreier Curves Over Finite Fields
Number Theory
2022-03-22 v1 Algebraic Geometry
Abstract
We study a mass formula for Artin--Schreier curves of genus defined over a finite field of characteristic . For an odd prime and for small , we determine the number of -isomorphism classes of Artin-Schreier curves of genus , weighted by the order of the centralizer of the Artin-Schreier involution in the automorphism group. This extends earlier results by several authors in characteristic . Keywords: Artin-Schreier curve, finite field, automorphism, Mass formula, moduli space, arithmetic statistics
Keywords
Cite
@article{arxiv.2203.10187,
title = {A Mass Formula For Artin--Schreier Curves Over Finite Fields},
author = {Anne M. Ho and Rachel Pries},
journal= {arXiv preprint arXiv:2203.10187},
year = {2022}
}