Resumen de Classification of quotient bundles on the Fargues–Fontaine curve

Serin Hong

• 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 subsheaves of a given vector bundle. For the proof, we combine the dimension counting argument for moduli of bundle maps developed in Birkbeck et al. (J Inst Math Jussieu 21:487–532, 2022) with a series of reduction arguments based on some reinterpretation of the classifying conditions.