$p$-adic Geometry (University Lecture Series)

Matthew Baker, Brian Conrad, Samit Dasgupta, Kiran S. Kedlaya, Jeremy Teitelbaum, edited by David Savitt, and Dinesh S. Thakur

ISBN 10: 0821844687 / ISBN 13: 9780821844687

Published by American Mathematical Society, 2008

About this Item

Offers a discussion of the Berkovich projective line and $p$-adic potential theory on that and more general Berkovich curves. This book discusses theoretical and computational aspects of $p$-adic cohomology and the zeta functions of varieties. It is suitable for students interested in learning about the techniques of $p$-adic geometry. Series: University Lecture Series. Num Pages: 203 pages, illustrations. BIC Classification: PBMW. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 259 x 215 x 14. Weight in Grams: 398. . 2008. Paperback. . . . . Books ship from the US and Ireland.

Seller Inventory # V9780821844687

Bibliographic Details

• Title: $p$-adic Geometry (University Lecture Series)
• Publisher: American Mathematical Society
• Publication Date: 2008
• Language: English
• ISBN 10: 0821844687
• ISBN 13: 9780821844687
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.