Number Theory Seminar

Vector bundles on the Fargues-Fontaine curve play a pivotal role in recent development of p-adic Hodge theory, as they provide geometric interpretations of many constructions in the field. In this talk, we give a complete classification of extensions between semi-stable vector bundles on the Fargues-Fontaine curve, in terms of a simple condition on Harder-Narasimhan polygons. The key ingredient of our proof is Scholze's language of diamonds, which allows us to define and study various moduli spaces of bundle maps. This is joint work with C. Birkbeck, T. Feng, D. Hansen, Q. Li, A. Wang, and L. Ye.