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تسجيل مستخدم جديدExtensions of Vector Bundles on the Fargues-Fontaine Curve
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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 polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholzes 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 Harder-Narasimhan polygons.
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