
Berkeley Lectures on p-adic Geometry
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
More details
Other editions
Additional editions


Persons
Content
- 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
- 8.4 The example of Spd Qp
- Lecture 9: Diamonds II
- 9.1 Complements on the pro-étale topology
- 9.2 Quasi-pro-étale morphisms
- 9.3 G-torsors
- 9.4 The diamond Spd Qp
- Lecture 10: Diamonds associated with adic spaces
- 10.1 The functor X ? X^?
- 10.2 Example: Rigid spaces
- 10.3 The underlying topological space of diamonds
- 10.4 The étale site of diamonds
- Appendix: Cohomology of local systems
- Lecture 11: Mixed-characteristic shtukas
- 11.1 The equal characteristic story: Drinfeld's shtukas and local shtukas
- 11.2 The adic space "S × Spa Zp"
- 11.3 Sections of (S × Spa Zp)^? S
- 11.4 Definition of mixed-characteristic shtukas
- Lecture 12: Shtukas with one leg
- 12.1 p-divisible groups over OC
- 12.2 Shtukas with one leg and p-divisible groups: An overview
- 12.3 Shtukas with no legs, and f-modules over the integral Robba ring
- 12.4 Shtukas with one leg, and BdR-modules
- Lecture 13: Shtukas with one leg II
- 13.1 Y is an adic space
- 13.2 The extension of shtukas over xL
- 13.3 Full faithfulness
- 13.4 Essential surjectivity
- 13.5 The Fargues-Fontaine curve
- Lecture 14: Shtukas with one leg III
- 14.1 Fargues' theorem
- 14.2 Extending vector bundles over the closed point of Spec Ainf
- 14.3 Proof of Theorem 14.2.1
- 14.4 Description of the functor "?"
- Appendix: Integral p-adic Hodge theory
- 14.6 Cohomology of rigid-analytic spaces
- 14.7 Cohomology of formal schemes
- 14.8 p-divisible groups
- 14.9 The results of [BMS18]
- Lecture 15: Examples of diamonds
- 15.1 The self-product Spd Qp × Spa Qp
- 15.2 Banach-Colmez spaces
- Lecture 16: Drinfeld's lemma for diamonds
- 16.1 The failure of p1(X × Y) = p1(X) × p1(Y)
- 16.2 Drinfeld's lemma for schemes
- 16.3 Drinfeld's lemma for diamonds
- Lecture 17: The v-topology
- 17.1 The v-topology on Perfd
- 17.2 Small v-sheaves
- 17.3 Spatial v-sheaves
- 17.4 Morphisms of v-sheaves
- Appendix: Dieudonné theory over perfectoid rings
- Lecture 18: v-sheaves associated with perfect and formal schemes
- 18.1 Definition
- 18.2 Topological spaces
- 18.3 Perfect schemes
- 18.4 Formal schemes
- Lecture 19: The B^+dR-affine Grassmannian
- 19.1 Definition of the B^+dR-affine Grassmannian
- 19.2 Schubert varieties
- 19.3 The Demazure resolution
- 19.4 Minuscule Schubert varieties
- Appendix: G-torsors
- Lecture 20: Families of affine Grassmannians
- 20.1 The convolution affine Grassmannian
- 20.2 Over Spd Qp
- 20.3 Over Spd Zp
- 20.4 Over Spd Qp × . . . × Spd Qp
- 20.5 Over Spd Zp × . . . × Spd Zp
- Lecture 21: Affine flag varieties
- 21.1 Over Fp
- 21.2 Over Zp
- 21.3 Affine flag varieties for tori
- 21.4 Local models
- 21.5 Dévissage
- Appendix: Examples
- 21.7 An EL case
- 21.8 A PEL case
- Lecture 22: Vector bundles and G-torsors
- 22.1 Vector bundles
- 22.2 Semicontinuity of the Newton polygon
- 22.3 The étale locus
- 22.4 Classification of G-torsors
- 22.5 Semicontinuity of the Newton point
- 22.6 Extending G-torsors
- Lecture 23: Moduli spaces of shtukas
- 23.1 Definition of mixed-characteristic local shtukas
- 23.2 The case of no legs
- 23.3 The case of one leg
- 23.4 The case of two legs
- 23.5 The general case
- Lecture 24: Local Shimura varieties
- 24.1 Definition of local Shimura varieties
- 24.2 Relation to Rapoport-Zink spaces
- 24.3 General EL and PEL data
- Lecture 25: Integral models of local Shimura varieties
- 25.1 Definition of the integral models
- 25.2 The case of tori
- 25.3 Non-parahoric groups
- 25.4 The EL case
- 25.5 The PEL case
- Bibliography
- Index
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.