- 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 Mixed-characteristic 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 v-topology -
Lecture 18 v-sheaves associated with perfect and formal schemes -
Lecture 19 The -affine Grassmannian -
Lecture 20 Families of affine Grassmannians -
Lecture 21 Affine flag varieties -
Lecture 22 Vector bundles and G-torsors on the relative Fargues-Fontaine curve -
Lecture 23 Moduli spaces of shtukas -
Lecture 24 Local Shimura varieties -
Lecture 25 Integral models of local Shimura varieties - Bibliography
- Index
Examples of adic spaces
Examples of adic spaces
- Chapter:
- (p.27) Lecture 4 Examples of adic spaces
- Source:
- Berkeley Lectures on p-adic Geometry
- Author(s):
Peter Scholze
Jared Weinstein
- Publisher:
- Princeton University Press
This chapter discusses various examples of adic spaces. These examples include the adic closed unit disc; the adic affine line; the closure of the adic closed unit disc in the adic affine line; the open unit disc; the punctured open unit disc; and the constant adic space associated to a profinite set. The chapter focuses on one example: the adic open unit disc over Zp. The adic spectrum Spa Zp consists of two points, a special point and a generic point. The chapter then studies the structure of analytic points. It also clarifies the relations between analytic rings and Tate rings.
Keywords: adic spaces, adic closed unit disc, adic affine line, adic open unit disc, adic spectrum, analytic points, analytic rings, Tate rings
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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 Mixed-characteristic 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 v-topology -
Lecture 18 v-sheaves associated with perfect and formal schemes -
Lecture 19 The -affine Grassmannian -
Lecture 20 Families of affine Grassmannians -
Lecture 21 Affine flag varieties -
Lecture 22 Vector bundles and G-torsors on the relative Fargues-Fontaine curve -
Lecture 23 Moduli spaces of shtukas -
Lecture 24 Local Shimura varieties -
Lecture 25 Integral models of local Shimura varieties - Bibliography
- Index