Perfectoidness of moduli spaces of quotient bundles on the FF curve

Abstract

Let F/ℚₚ be a finite extension and let C be a fixed complete algebraically closed field containing F̆. For 0 < d < n, let W_n,d denote the v-sheaf parametrizing quotient bundles 𝒪(1/n) ↠ ℰ on the relative Fargues–Fontaine curve whose geometric fibres are isomorphic to 𝒪(1/d). We prove that W_n,d is represented by a perfectoid space. This is Conjecture 5.4 in [HM].

Topics

• p-adic geometry
• Perfectoid spaces
• v-sheaves
• Fargues–Fontaine curve
• Quotient bundles
• Vector bundles

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