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.

中文翻译：

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Fargues-Fontaine 曲线上子束的分类

我们在 Fargues-Fontaine 曲线上对给定向量丛的所有子丛进行完全分类，其中子丛是指局部自由子层。我们的分类是根据 Harder-Narasimhan 多边形的一个简单而明确的条件给出的。我们的证明受到我们之前工作（Hong 2019）中主要定理证明的启发，但也涉及一些重要的调整。