Vol. 16, No. 2, 2022

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

Volume 18, 1 issue

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
Editorial Board
Editors’ Interests
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.
Descent on elliptic surfaces and arithmetic bounds for the Mordell–Weil rank

Jean Gillibert and Aaron Levin

Vol. 16 (2022), No. 2, 311–333

We introduce the use of p-descent techniques for elliptic surfaces over a perfect field of characteristic not 2 or 3. Under mild hypotheses, we obtain an upper bound for the rank of a nonconstant elliptic surface. When p = 2, this bound is an arithmetic refinement of a well-known geometric bound for the rank deduced from Igusa’s inequality. This answers a question raised by Ulmer. We give some applications to rank bounds for elliptic surfaces over the rational numbers.

PDF Access Denied

We have not been able to recognize your IP address 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:

elliptic surfaces, Mordell–Weil rank, Igusa's inequality, $p$-descent
Mathematical Subject Classification
Primary: 14D10
Secondary: 14G25, 14K15
Received: 30 April 2020
Revised: 23 April 2021
Accepted: 17 June 2021
Published: 27 April 2022
Jean Gillibert
Institut de Mathématiques de Toulouse
Aaron Levin
Department of Mathematics
Michigan State University
East Lansing, MI
United States