Classification of subbundles on the Fargues-Fontaine curve

TL;DR

This paper provides a complete classification of all subbundles of vector bundles on the Fargues-Fontaine curve using explicit conditions on Harder-Narasimhan polygons, advancing understanding in p-adic geometry.

Contribution

It offers a new, explicit classification criterion for subbundles on the Fargues-Fontaine curve, extending prior theoretical results with concrete conditions.

Findings

Complete classification of subbundles achieved

Explicit conditions on Harder-Narasimhan polygons established

Proof involves novel adjustments inspired by previous work

Abstract

We completely classify all subbundles of a given vector bundle on the Fargues-Fontaine curve. 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 [Hon19], but also involves a number of nontrivial adjustments.