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 ; no. 207.

Annals of mathematics studies ; number 207

Language:

English

Subjects (All):

Arithmetical algebraic geometry.

p-adic analysis.

Geometry, Algebraic.

Physical Description:

x, 250 pages ; 24 cm.

Place of Publication:

Princeton, NJ : Princeton University Press, [2020]

Summary:

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze 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, Scholze 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. In this book, Peter Scholze and Jared Weinstein show 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. 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. Publisher's description.

Contents:

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.

Notes:

Includes bibliographical references [pages 241-248] and index.

ISBN:

9780691202099

0691202095

9780691202082

0691202087

OCLC:

1125990643