Berkeley Lectures on padic Geometry (eBook)
by peter scholze, jared weinstein (Author)

 264 Pages
Berkeley Lectures on padic 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 padic 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 mixedcharacteristic 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 mixedcharacteristic 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 padic field.
This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores padic 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 pdivisible groups, padic Hodge theory, and RapoportZink spaces, are thoroughly explained. Berkeley Lectures on padic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
 Released: May 12, 2020
 Categories: Education
 Language: English
 Publisher: Princeton University Press
 ISBN10: 069120215X
 ISBN13: 9780691202150