 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
The BdR+affine Grassmannian
The BdR+affine Grassmannian
 Chapter:
 (p.169) Lecture 19 The ${B}_{\text{dR}}^{+}$affine Grassmannian
 Source:
 Berkeley Lectures on padic Geometry
 Author(s):
Peter Scholze
Jared Weinstein
 Publisher:
 Princeton University Press
This chapter defines an object that was one of the big motivations to develop a theory of diamonds. In the study of the usual Grassmannian variety G/B attached to a reductive group G, one defines a Schubert variety to be the closure of a Borbit in G/B. Generally, Schubert varieties are singular varieties. Desingularizations of Schubert varieties are constructed by Demazure. The chapter uses an analogue of this construction in the context of the B^{+}_{dR}Grassmannian. It then looks at miniscule Schubert varieties. In this case, one can identify the space explicitly. If µ is minuscule, the Bialynicki–Birula map is an isomorphism.
Keywords: diamonds, Grassmannian variety, Schubert varieties, singular varieties, desingularizations, Demazure, Bialynicki–Birula map, isomorphism
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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