Berkeley Lectures on p-adic Geometry: (AMS-207)
Peter Scholze and Jared Weinstein
Abstract
This book presents an important breakthrough in arithmetic geometry. In 2014, this book'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 ... More
This book presents an important breakthrough in arithmetic geometry. In 2014, this book'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 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.
Keywords:
arithmetic geometry,
p-adic geometry,
perfectoid spaces,
diamonds,
mixed-characteristic shtukas,
moduli spaces,
p-divisible groups,
p-adic Hodge theory,
Rapoport-Zink spaces
Bibliographic Information
| Print publication date: 2020 |
Print ISBN-13: 9780691202082 |
| Published to Princeton Scholarship Online: January 2021 |
DOI:10.23943/princeton/9780691202082.001.0001 |
Authors
Affiliations are at time of print publication.
Peter Scholze, author
University of Bonn
Jared Weinstein, author
Boston University
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