Berkeley lectures on p-adic geometry / Peter Scholze and Jared Weinstein.

Format:

Book

Author/Creator:

Scholze, Peter, author.

Weinstein, Jared, author.

Series:

Annals of mathematics studies ; 207.

Annals of mathematics studies ; 207

Language:

English

Subjects (All):

p-adic analysis.

Physical Description:

1 online resource (x, 250 pages).

Place of Publication:

Princeton : Princeton University Press, 2021.

Summary:

This text presents an important breakthrough in arithmetic geometry. In 2014, this work's author delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, the author introduced the concept of 'diamonds,' which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. This book shows that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. The text follows the informal style of the original Berkeley lectures, with one chapter per lecture.

Contents:

Frontmatter

Contents

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 B+dR-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

Notes:

Previously issued in print: 2020.

Includes bibliographical references and index.

Description based on print version record and CIP data provided by publisher; resource not viewed.

ISBN:

9780691202150

069120215X

OCLC:

1198931001