Berkeley Lectures on p-adic Geometry : : (AMS-207) / / Peter Scholze, Jared Weinstein.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English
• VerfasserIn: Scholze, Peter,; Weinstein, Jared,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2020]; ©2020
• Year of Publication: 2020
• Language: English
• Series: Annals of Mathematics Studies ; 207
• Physical Description: 1 online resource (264 p.) :; 5 b/w illus.

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.

Table of 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