Berkeley Lectures on p-adic Geometry: (AMS-207)
By Peter Scholze and Jared Weinstein
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About this ebook
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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Titles in the series (100)
Algebraic Theory of Numbers. (AM-1), Volume 1 Rating: 0 out of 5 stars0 ratingsDegree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-22), Volume 2: The Geometry of Orthogonal Spaces. (AM-22) Rating: 0 out of 5 stars0 ratingsThe Calculi of Lambda-Conversion (AM-6), Volume 6 Rating: 4 out of 5 stars4/5Consistency of the Continuum Hypothesis. (AM-3), Volume 3 Rating: 0 out of 5 stars0 ratingsFinite Dimensional Vector Spaces. (AM-7), Volume 7 Rating: 4 out of 5 stars4/5Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) Rating: 0 out of 5 stars0 ratingsTranscendental Numbers. (AM-16) Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-28), Volume II Rating: 0 out of 5 stars0 ratingsExistence Theorems in Partial Differential Equations. (AM-23), Volume 23 Rating: 0 out of 5 stars0 ratingsCurvature and Betti Numbers. (AM-32), Volume 32 Rating: 0 out of 5 stars0 ratingsIsoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27 Rating: 0 out of 5 stars0 ratingsTopics in Topology. (AM-10), Volume 10 Rating: 0 out of 5 stars0 ratingsIntroduction to Non-Linear Mechanics. (AM-11), Volume 11 Rating: 0 out of 5 stars0 ratingsA Theory of Cross-Spaces. (AM-26), Volume 26 Rating: 0 out of 5 stars0 ratingsProbleme General de la Stabilite du Mouvement. (AM-17), Volume 17 Rating: 0 out of 5 stars0 ratingsThe Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5 Rating: 0 out of 5 stars0 ratingsLectures on Differential Equations. (AM-14), Volume 14 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-20), Volume I Rating: 0 out of 5 stars0 ratingsConvergence and Uniformity in Topology. (AM-2), Volume 2 Rating: 0 out of 5 stars0 ratingsAn Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4 Rating: 0 out of 5 stars0 ratingsAn Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18 Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-21), Volume 1: Measures and Integrals. (AM-21) Rating: 0 out of 5 stars0 ratingsOrder-Preserving Maps and Integration Processes. (AM-31), Volume 31 Rating: 0 out of 5 stars0 ratingsSurface Area. (AM-35), Volume 35 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Partial Differential Equations. (AM-33), Volume 33 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-24), Volume I Rating: 0 out of 5 stars0 ratingsTopological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15 Rating: 0 out of 5 stars0 ratingsLectures on Fourier Integrals. (AM-42), Volume 42 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Riemann Surfaces. (AM-30), Volume 30 Rating: 0 out of 5 stars0 ratings
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