Softcover ISBN:  9780821844687 
Product Code:  ULECT/45 
203 pp 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 
Electronic ISBN:  9781470418366 
Product Code:  ULECT/45.E 
203 pp 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 

Book DetailsUniversity Lecture SeriesVolume: 45; 2008MSC: Primary 14; Secondary 11;
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 nonarchimedean 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.ReadershipGraduate students and research mathematicians interested in number theory and algebraic geometry.

Table of Contents

Articles

Vladimir Berkovich  Nonarchimedean analytic geometry: first steps

Brian Conrad  Chapter 1. Several approaches to nonarchimedean geometry

Samit Dasgupta and Jeremy Teitelbaum  Chapter 2. The $p$adic upper half plane

Matthew Baker  Chapter 3. An introduction to Berkovich analytic spaces and nonarchimedean potential theory on curves

Kiran S. Kedlaya  Chapter 4. $p$adic cohomology: from theory to practice


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

Articles

Vladimir Berkovich  Nonarchimedean analytic geometry: first steps

Brian Conrad  Chapter 1. Several approaches to nonarchimedean geometry

Samit Dasgupta and Jeremy Teitelbaum  Chapter 2. The $p$adic upper half plane

Matthew Baker  Chapter 3. An introduction to Berkovich analytic spaces and nonarchimedean potential theory on curves

Kiran S. Kedlaya  Chapter 4. $p$adic cohomology: from theory to practice