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Berkeley lectures on p-adic geometry /

Bibliographic Details
Main Authors: Scholze, Peter (Author), Weinstein, Jared (Author)
Format: eBook
Language:English
Published: Princeton, NJ : Princeton University Press, [2020]
Series:Annals of mathematics studies.
Subjects:
Arithmetical algebraic geometry.
p-adic analysis.
Geometry, Algebraic.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Title
  • Copyright
  • Contents
  • Foreword
  • Lecture 1: Introduction
  • 1.1 Motivation: Drinfeld, L. Lafforgue, and V. Lafforgue
  • 1.2 The possibility of shtukas in mixed characteristic
  • Lecture 2: Adic spaces
  • 2.1 Motivation: Formal schemes and their generic fibers
  • 2.2 Huber rings
  • 2.3 Continuous valuations
  • Lecture 3: Adic spaces II
  • 3.1 Rational Subsets
  • 3.2 Adic spaces
  • 3.3 The role of A^+
  • 3.4 Pre-adic spaces
  • Appendix: Pre-adic spaces
  • Lecture 4: Examples of adic spaces
  • 4.1 Basic examples
  • 4.2 Example: The adic open unit disc over Zp
  • 4.3 Analytic points
  • Lecture 5: Complements on adic spaces
  • 5.1 Adic morphisms
  • 5.2 Analytic adic spaces
  • 5.3 Cartier divisors
  • Lecture 6: Perfectoid rings
  • 6.1 Perfectoid Rings
  • 6.2 Tilting
  • 6.3 Sousperfectoid rings
  • Lecture 7: Perfectoid spaces
  • 7.1 Perfectoid spaces: Definition and tilting equivalence
  • 7.2 Why do we study perfectoid spaces?
  • 7.3 The equivalence of étale sites
  • 7.4 Almost mathematics, after Faltings
  • 7.5 The étale site
  • Lecture 8: Diamonds
  • 8.1 Diamonds: Motivation
  • 8.2 Pro-étale morphisms
  • 8.3 Definition of diamonds