Vol. 15, No. 5, 2021
Download this article
Download this article For screen
For printing
Recent Issues

Volume 19, 1 issue

Volume 18, 12 issues

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 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
Classification of subbundles on the Fargues–Fontaine curve

Serin Hong
Vol. 15 (2021), No. 5, 1127–1156
DOI: 10.2140/ant.2021.15.1127
Abstract

We completely classify all subbundles of a given vector bundle on the Fargues–Fontaine curve, where by a subbundle we mean a locally free subsheaf. Our classification is given in terms of a simple and explicit condition on Harder–Narasimhan polygons. Our proof is inspired by the proof of the main theorem in our previous work (Hong 2019), but also involves a number of nontrivial adjustments.

Keywords
Fargues–Fontaine curve, vector bundles, classification
Mathematical Subject Classification 2010
Primary: 14H60
Secondary: 11G20, 14D20, 14G22
Milestones
Received: 13 November 2019
Revised: 17 March 2020
Accepted: 12 December 2020
Published: 30 June 2021
Authors
Serin Hong
Serin Hong
University of Michigan
Ann Arbor, MI
United States