P-adic Geometry

by Baker, Matthew; Conrad, Brian; Dasgupta, Samit; Kedlaya, Kiran S.; Teitelbaum, Jeremy

• ISBN13: 9780821844687
• ISBN10: 0821844687
• Format: Paperback
• Copyright: 2008-09-26
• Publisher: Amer Mathematical Society

Summary

"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 Schoo1 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."--BOOK JACKET.

Table of Contents

Non-archimedean analytic geometry: first steps

Several approaches to non-archimedean geometry

The $p$-adic upper half plane

An Introduction to Berkovich analytic spaces and non-archimedean potential theory on curves

$p$-adic cohomology: from theory to practice

Table of Contents provided by Publisher. All Rights Reserved.