a-numbers of curves in Artin–Schreier covers

Booher, Jeremy; Cais, Bryden

doi:10.2140/ant.2020.14.593

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-7833 (e-only)

ISSN: 1937-0652 (print)

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

$a$-numbers of curves in Artin–Schreier covers

Jeremy Booher and Bryden Cais

Vol. 14 (2020), No. 3, 587–641

DOI: 10.2140/ant.2020.14.593

Abstract

Let $π : Y \to X$ be a branched $Z ∕ p Z$ -cover of smooth, projective, geometrically connected curves over a perfect field of characteristic $p > 0$ . We investigate the relationship between the $a$ -numbers of $Y$ and $X$ and the ramification of the map $π$ . This is analogous to the relationship between the genus (respectively $p$ -rank) of $Y$ and $X$ given the Riemann–Hurwitz (respectively Deuring–Shafarevich) formula. Except in special situations, the $a$ -number of $Y$ is not determined by the $a$ -number of $X$ and the ramification of the cover, so we instead give bounds on the $a$ -number of $Y$ . We provide examples showing our bounds are sharp. The bounds come from a detailed analysis of the kernel of the Cartier operator.

PDF Access Denied

We have not been able to recognize your IP address 18.226.28.197 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

$a$-numbers, Artin–Schreier covers, arithmetic geometry, covers of curves, invariants of curves

Mathematical Subject Classification 2010

Primary: 14G17

Secondary: 11G20, 14H40

Milestones

Received: 26 July 2018

Revised: 2 September 2019

Accepted: 7 October 2019

Published: 1 June 2020

Authors

Jeremy Booher
School of Mathematics and Statistics University of Canterbury Christchurch New Zealand

Bryden Cais
Department of Mathematics University of Arizona Tucson, AZ United States

Vol. 14, No. 3, 2020