Berkeley Lectures on p-adic Geometry
eBook - PDF

Berkeley Lectures on p-adic Geometry

  1. 264 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Berkeley Lectures on p-adic Geometry

About this book

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.

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Yes, you can access Berkeley Lectures on p-adic Geometry by Peter Scholze,Jared Weinstein in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebraic Geometry. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Foreword
  6. Lecture 1: Introduction
  7. Lecture 2: Adic spaces
  8. Lecture 3: Adic spaces II
  9. Lecture 4: Examples of adic spaces
  10. Lecture 5: Complements on adic spaces
  11. Lecture 6: Perfectoid rings
  12. Lecture 7: Perfectoid spaces
  13. Lecture 8: Diamonds
  14. Lecture 9: Diamonds II
  15. Lecture 10: Diamonds associated with adic spaces
  16. Lecture 11: Mixed-characteristic shtukas
  17. Lecture 12: Shtukas with one leg
  18. Lecture 13: Shtukas with one leg II
  19. Lecture 14: Shtukas with one leg III
  20. Lecture 15: Examples of diamonds
  21. Lecture 16: Drinfeld's lemma for diamonds
  22. Lecture 17: The v-topology
  23. Lecture 18: v-sheaves associated with perfect and formal schemes
  24. Lecture 19: The B^+dR-affine Grassmannian
  25. Lecture 20: Families of affine Grassmannians
  26. Lecture 21: Affine flag varieties
  27. Lecture 22: Vector bundles and G-torsors
  28. Lecture 23: Moduli spaces of shtukas
  29. Lecture 24: Local Shimura varieties
  30. Lecture 25: Integral models of local Shimura varieties
  31. Bibliography
  32. Index