Classification of quotient bundles on the Fargues-Fontaine curve

TL;DR

This paper provides a complete classification of quotient bundles on the Fargues-Fontaine curve, along with related classifications of vector bundles generated by global sections and subbundles, using dimension counting and reduction techniques.

Contribution

It introduces a comprehensive classification framework for quotient bundles on the Fargues-Fontaine curve, extending to related bundle classifications with novel proof methods.

Findings

Complete classification of quotient bundles on the Fargues-Fontaine curve

Classification of vector bundles generated by fixed global sections

Near-complete classification of subbundles

Abstract

We completely classify all quotient bundles of a given vector bundle on the Fargues-Fontaine curve. As consequences, we have two additional classification results: a complete classification of all vector bundles that are generated by a fixed number of global sections and a nearly complete classification of subbundles of a given vector bundle. For the proof, we combine the dimension counting argument for moduli of bundle maps developed in [BFH+17] with a series of reduction arguments based on some reinterpretation of the classifying conditions.