Berkeley Lectures on P-Adic Geometry - Paperback

by Peter Scholze (Author), Jared Weinstein (Author)

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.

Author Biography

Peter Scholze is a professor at the University of Bonn and director of the Max Planck Institute for Mathematics. Jared Weinstein is associate professor of mathematics at Boston University.