Vol. 15, No. 5, 2021

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Classification of subbundles on the Fargues–Fontaine curve

Serin Hong

Vol. 15 (2021), No. 5, 1127–1156
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