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Classification of subbundles on the Fargues–Fontaine curve
Algebra & Number Theory  (IF0.938),  Pub Date : 2021-06-30, DOI: 10.2140/ant.2021.15.1127
Serin Hong

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.