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\(p\)-adic Geometry: Lectures from the 2007 Arizona Winter School
Matthew Baker, Georgia Institute of Technology, Atlanta, GA, Brian Conrad, University of Michigan, Ann Arbor, MI, Samit Dasgupta, Harvard University, Cambridge, MA, Kiran S. Kedlaya, Massachusetts Institute of Technology, Cambridge, MA, Jeremy Teitelbaum, University of Illinois at Chicago, IL, and edited by David Savitt and Dinesh S. Thakur, University of Arizona, Tucson, AZ
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University Lecture Series
2008; 203 pp; softcover
Volume: 45
ISBN-10: 0-8218-4468-7
ISBN-13: 978-0-8218-4468-7
List Price: US$46
Member Price: US$36.80
Order Code: ULECT/45
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In recent decades, \(p\)-adic geometry and \(p\)-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter School 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject.

Following invaluable introductions by John Tate and Vladimir Berkovich, two pioneers of non-archimedean geometry, Brian Conrad's chapter introduces the general theory of Tate's rigid analytic spaces, Raynaud's view of them as the generic fibers of formal schemes, and Berkovich spaces. Samit Dasgupta and Jeremy Teitelbaum discuss the \(p\)-adic upper half plane as an example of a rigid analytic space and give applications to number theory (modular forms and the \(p\)-adic Langlands program). Matthew Baker offers a detailed discussion of the Berkovich projective line and \(p\)-adic potential theory on that and more general Berkovich curves. Finally, Kiran Kedlaya discusses theoretical and computational aspects of \(p\)-adic cohomology and the zeta functions of varieties. This book will be a welcome addition to the library of any graduate student and researcher who is interested in learning about the techniques of \(p\)-adic geometry.

Readership

Graduate students and research mathematicians interested in number theory and algebraic geometry.

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