Powers of the Cartier operator on Artin-Schreier covers
Number Theory
2024-07-29 v2
Abstract
Curves in positive characteristic have a Cartier operator acting on their space of regular differentials. The -number of a curve is defined to be the dimension of the kernel of the Cartier operator. In \cite{BoCaASc}, Booher and Cais used a sheaf-theoretic approach to give bounds on the -numbers of Artin-Schreier covers. In this paper, that approach is generalized to arbitrary powers of the Cartier operator, yielding bounds for the dimension of the kernel. These bounds give new restrictions on the Ekedahl-Oort type of Artin-Schreier covers.
Keywords
Cite
@article{arxiv.2208.06504,
title = {Powers of the Cartier operator on Artin-Schreier covers},
author = {Steven R. Groen},
journal= {arXiv preprint arXiv:2208.06504},
year = {2024}
}
Comments
This is the version that has been published in International Journal of Number Theory