On certain extensions of vector bundles in p-adic geometry

Abstract

Given three arbitrary vector bundles on the Fargues-Fontaine curve where one of them is assumed to be semistable, we give an explicit and complete criterion in terms of Harder-Narasimhan polygons on whether there exists a short exact sequence among them. Our argument is based on a dimension analysis of certain moduli spaces of bundle maps and bundle extensions using Scholze's theory of diamonds.