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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 gg defined over a finite field kk of characteristic pp. For an odd prime pp and for small gg, we determine the number of kk-isomorphism classes of Artin-Schreier curves of genus gg, 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 p=2p=2. 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}
}