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Berkeley Lectures on p-adic Geometry(AMS-207)$
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Peter Scholze and Jared Weinstein

Print publication date: 2020

Print ISBN-13: 9780691202082

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691202082.001.0001

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Shtukas with one leg III

Shtukas with one leg III

(p.115) Lecture 14 Shtukas with one leg III
Berkeley Lectures on p-adic Geometry

Peter Scholze

Jared Weinstein

Princeton University Press

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.

Keywords:   one-legged shtukas, Fargues' theorem, finite free Ainf-modules, vector bundles, local ring, finite free R-modules

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