Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
$p$-groups, $p$-rank, and semistable reduction of coverings of curves

Yu Yang

Vol. 18 (2024), No. 2, 281–317
Abstract

We prove various explicit formulas concerning p-rank of p-coverings of pointed semistable curves over discrete valuation rings. In particular, we obtain a full generalization of Raynaud’s formula for p-rank of fibers over nonmarked smooth closed points in the case of arbitrary closed points. As an application, for abelian p-coverings, we give an affirmative answer to an open problem concerning boundedness of p-rank asked by Saïdi more than twenty years ago.

Keywords
$p$-rank, semistable reduction, pointed semistable curve, pointed semistable covering
Mathematical Subject Classification
Primary: 14E20, 14G17
Secondary: 14G20, 14H30
Milestones
Received: 18 April 2022
Revised: 22 September 2022
Accepted: 13 April 2023
Published: 6 February 2024
Authors
Yu Yang
Research Institute for Mathematical Sciences
Kyoto University
Kyoto
Japan

Open Access made possible by participating institutions via Subscribe to Open.