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- Title
EXTENSIONS OF VECTOR BUNDLES ON THE FARGUES-FONTAINE CURVE.
- Authors
Birkbeck, Christopher; Feng, Tony; Hansen, David; Hong, Serin; Li, Qirui; Wang, Anthony; Ye, Lynnelle
- 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.
- Publication
Journal of the Institute of Mathematics of Jussieu, 2022, Vol 21, Issue 2, p487
- ISSN
1474-7480
- Publication type
Article
- DOI
10.1017/S1474748020000183