 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
Introduction
Introduction
 Chapter:
 (p.1) Lecture 1 Introduction
 Source:
 (p.iii) Berkeley Lectures on padic Geometry
 Author(s):
Peter Scholze
Jared Weinstein
 Publisher:
 Princeton University Press
This introductory chapter provides an overview of Drinfeld's work on the global Langlands correspondence over function fields. Whereas the global Langlands correspondence is largely open in the case of number fields K, it is a theorem for function fields, due to Drinfeld and L. Lafforgue. The key innovation in this case is Drinfeld's notion of an Xshtuka (or simply shtuka). The Langlands correspondence for X is obtained by studying moduli spaces of shtukas. A large part of this course is about the definition of perfectoid spaces and diamonds. There is an important special case where the moduli spaces of shtukas are classical rigidanalytic spaces. This is the case of local Shimura varieties. Some examples of these are the RapoportZink spaces.
Keywords: Langlands correspondence, function fields, shtukas, moduli spaces, perfectoid spaces, perfectoid diamonds, local Shimura varieties, RapoportZink spaces
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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