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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, Chicago, IL
Edited by: David Savitt University of Arizona, Tucson, AZ
Dinesh S. Thakur University of Arizona, Tucson, AZ
Front Cover for $p$-adic Geometry
Available Formats:
Softcover ISBN: 978-0-8218-4468-7
Product Code: ULECT/45
203 pp 
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
Electronic ISBN: 978-1-4704-1836-6
Product Code: ULECT/45.E
203 pp 
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Front Cover for $p$-adic Geometry
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  • Front Cover for $p$-adic Geometry
  • Back Cover for $p$-adic Geometry
$p$-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, Chicago, IL
Edited by: David Savitt University of Arizona, Tucson, AZ
Dinesh S. Thakur University of Arizona, Tucson, AZ
Available Formats:
Softcover ISBN:  978-0-8218-4468-7
Product Code:  ULECT/45
203 pp 
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
Electronic ISBN:  978-1-4704-1836-6
Product Code:  ULECT/45.E
203 pp 
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
  • Book Details
     
     
    University Lecture Series
    Volume: 452008
    MSC: 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 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.

  • Table of Contents
     
     
    • Articles
    • Vladimir Berkovich - Non-archimedean analytic geometry: first steps
    • Brian Conrad - Chapter 1. Several approaches to non-archimedean 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 non-archimedean potential theory on curves
    • Kiran S. Kedlaya - Chapter 4. $p$-adic cohomology: from theory to practice
  • Additional Material
     
     
  • Request Review Copy
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Volume: 452008
MSC: 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 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.

  • Articles
  • Vladimir Berkovich - Non-archimedean analytic geometry: first steps
  • Brian Conrad - Chapter 1. Several approaches to non-archimedean 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 non-archimedean potential theory on curves
  • Kiran S. Kedlaya - Chapter 4. $p$-adic cohomology: from theory to practice
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