Shtukas with one leg III

Abstract

This chapter presents a third lecture on one-legged shtukas. The goal is to complete the proof of Fargues' theorem. To complete the proof of Fargues' theorem, it remains to prove the following result, where Y = Spa Ainf REVERSE SOLIDUS {xk}. Theorem 14.2.1 posits that there is an equivalence of categories between finite free Ainf-modules and vector bundles on Y. One should think of this as being an analogue of a classical result: If (R, m) is a 2-dimensional regular local ring, then finite free R-modules are equivalent to vector bundles on (Spec R)REVERSE SOLIDUS {m}. The chapter then provides a proof of Theorem 14.2.1.