We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder-Narasimhan (HN) polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze's language of diamonds. This analysis reduces our main results to a somewhat involved combinatorial problem, which we then solve via a reinterpretation in terms of the Euclidean geometry of HN polygons.
|Number of pages||46|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|Early online date||14 May 2020|
|Publication status||Published - 14 Mar 2022|
- Vector bundles