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p-adic Geometry

p-adic Geometry

Lectures from the 2007 Arizona Winter School

by David SavittSamit Dasgupta Matthew Baker and others
Paperback
Publication Date: 30/10/2008

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$73.70
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.
ISBN:
9780821844687
9780821844687
Category:
Algebraic geometry
Format:
Paperback
Publication Date:
30-10-2008
Publisher:
American Mathematical Society
Country of origin:
United States
Pages:
203
Weight:
0.4kg
Matthew Baker

Matthew Baker is the author of the story collection Hybrid Creatures. His stories have appeared in the Paris Review, American Short Fiction, New England Review, One Story, Electric Literature and Conjunctions, and in anthologies including Best of the Net and Best Small Fictions.

A recipient of grants and fellowships from the Fulbright Commission and the MacDowell Colony, among many others, he has an MFA from Vanderbilt University, where he was the founding editor of Nashville Review. Born in Michigan, he currently lives in New York City.

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