 Title Pages
 Foreword

Lecture 1 Introduction 
Lecture 2 Adic spaces 
Lecture 3 Adic spaces II 
Lecture 4 Examples of adic spaces 
Lecture 5 Complements on adic spaces 
Lecture 6 Perfectoid rings 
Lecture 7 Perfectoid spaces 
Lecture 8 Diamonds 
Lecture 9 Diamonds II 
Lecture 10 Diamonds associated with adic spaces 
Lecture 11 Mixedcharacteristic shtukas 
Lecture 12 Shtukas with one leg 
Lecture 13 Shtukas with one leg II 
Lecture 14 Shtukas with one leg III 
Lecture 15 Examples of diamonds 
Lecture 16 Drinfeld’s lemma for diamonds 
Lecture 17 The vtopology 
Lecture 18 vsheaves associated with perfect and formal schemes 
Lecture 19 The ${B}_{\text{dR}}^{+}$affine Grassmannian 
Lecture 20 Families of affine Grassmannians 
Lecture 21 Affine flag varieties 
Lecture 22 Vector bundles and Gtorsors on the relative FarguesFontaine curve 
Lecture 23 Moduli spaces of shtukas 
Lecture 24 Local Shimura varieties 
Lecture 25 Integral models of local Shimura varieties  Bibliography
 Index
Shtukas with one leg II
Shtukas with one leg II
 Chapter:
 (p.108) Lecture 13 Shtukas with one leg II
 Source:
 Berkeley Lectures on padic Geometry
 Author(s):
Peter Scholze
Jared Weinstein
 Publisher:
 Princeton University Press
This chapter offers a second lecture on onelegged shtukas. It shows that a shtuka over Spa C^{b}, a priori defined over Y_{[0,INFINITY)} = Spa A_{inf} REVERSE SOLIDUS {x_{k}, x_{L}}, actually extends to Y = Spa A_{inf} REVERSE SOLIDUS {x_{k}}. In doing so, the chapter considers the theory of φmodules over the Robba ring, due to Kedlaya. These are in correspondence with vector bundles over the FarguesFontaine curve. The chapter then looks at the proposition that the space Y is an adic space. It also sketches a proof that the functor described in Theorem 13.2.1 is fully faithful. This is more general, and works if C is any perfectoid field (not necessarily algebraically closed).
Keywords: onelegged shtukas, shtukas, φmodules, Robba ring, Kedlaya, vector bundles, FarguesFontaine curve, adic space, perfectoid field
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 Title Pages
 Foreword

Lecture 1 Introduction 
Lecture 2 Adic spaces 
Lecture 3 Adic spaces II 
Lecture 4 Examples of adic spaces 
Lecture 5 Complements on adic spaces 
Lecture 6 Perfectoid rings 
Lecture 7 Perfectoid spaces 
Lecture 8 Diamonds 
Lecture 9 Diamonds II 
Lecture 10 Diamonds associated with adic spaces 
Lecture 11 Mixedcharacteristic shtukas 
Lecture 12 Shtukas with one leg 
Lecture 13 Shtukas with one leg II 
Lecture 14 Shtukas with one leg III 
Lecture 15 Examples of diamonds 
Lecture 16 Drinfeld’s lemma for diamonds 
Lecture 17 The vtopology 
Lecture 18 vsheaves associated with perfect and formal schemes 
Lecture 19 The ${B}_{\text{dR}}^{+}$affine Grassmannian 
Lecture 20 Families of affine Grassmannians 
Lecture 21 Affine flag varieties 
Lecture 22 Vector bundles and Gtorsors on the relative FarguesFontaine curve 
Lecture 23 Moduli spaces of shtukas 
Lecture 24 Local Shimura varieties 
Lecture 25 Integral models of local Shimura varieties  Bibliography
 Index