Classification of quotient bundles on the Fargues-Fontaine curve

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.

arXiv comment41 pages, 13 figures, with an appendix coauthored by Hannah Larson

References in corpus (3)

• Geometrization of the local Langlands correspondence: an overview
• Extensions of Vector Bundles on the Fargues-Fontaine Curve
• Classification of subbundles on the Fargues-Fontaine curve

Cited by in corpus (2)

• Classification of subbundles on the Fargues-Fontaine curve
• On certain extensions of vector bundles in p-adic geometry