EXTENSIONS OF VECTOR BUNDLES ON THE FARGUES-FONTAINE CURVE. (14th March 2022)

• Record Type: Journal Article
• Authors: Birkbeck, Christopher; Feng, Tony; Hansen, David; Hong, Serin; Li, Qirui; Wang, Anthony; Ye, Lynnelle
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 21:Number 2(2022)
• Page Start: 487
• Page End: 532
• Publication Date: 2022-03-14
• Subjects: Fargues–Fontaine -- Diamonds -- Vector bundles; 14D24 -- 14G45; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748020000183
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract: 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.