Berkeley lectures on ρ-adic geometry
Series: Annals of Mathematics Studies; no. 207Publication details: Princeton University Press, 2020. New Jersey:Description: x, 250 p. : ill. ; pb; 24 cmISBN:- 9780691202082
- 516.35 SCH
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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IIT Gandhinagar General Stacks | General | 516.35 SCH (Browse shelf(Opens below)) | 1 | Checked out | 16/12/2024 | 029689 |
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516.35 OGU Lectures on logarithmic algebraic geometry | 516.35 OLS Algebraic spaces and stacks | 516.35 RAM Gaṇitānanda: selected works of Radha Charan Gupta on history of mathematics | 516.35 SCH Berkeley lectures on ρ-adic geometry | 516.35 SOU Lectures on Arakelov geometry | 516.35 VOI Hodge theory and complex algebraic geometry, Vol. 2 | 516.35 VOS Hodge theory and complex algebraic geometry I, Vol. 1 |
Includes bibliographical references and index.
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 ρ-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 ρ-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores ρ-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 ρ-divisible groups, ρ-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on ρ-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
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