 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
Local Shimura varieties
Local Shimura varieties
 Chapter:
 (p.225) Lecture 24 Local Shimura varieties
 Source:
 Berkeley Lectures on padic Geometry
 Author(s):
Peter Scholze
Jared Weinstein
 Publisher:
 Princeton University Press
This chapter specializes the theory back to the case of local Shimura varieties, and explains the relation with RapoportZink spaces. It begins with a local Shimura datum. A local Shimura datum is a triple (G, b, µ) consisting of a reductive group G over Qp, a conjugacy class µ of minuscule cocharacters. RapoportZink spaces are moduli of deformations of a fixed pdivisible group. After reviewing these, the chapter shows that the diamond associated with the generic fiber of a RapoportZink space is isomorphic to a moduli space of shtukas of the form with µ minuscule. It then extends the results to general EL and PEL data.
Keywords: local Shimura varieties, RapoportZink spaces, local Shimura datum, minuscule cocharacters, pdivisible group, diamond, moduli space, shtukas, El data, PEL data
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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