Classification of subbundles on the Fargues–Fontaine curve

Hong, Serin

doi:10.2140/ant.2021.15.1127

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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.

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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

Vol. 15, No. 5, 2021