**University Lecture Series**

Volume: 45;
2008;
203 pp;
Softcover

MSC: Primary 14;
Secondary 11

**Print ISBN: 978-0-8218-4468-7
Product Code: ULECT/45**

List Price: $52.00

AMS Member Price: $41.60

MAA Member Price: $46.80

**Electronic ISBN: 978-1-4704-1836-6
Product Code: ULECT/45.E**

List Price: $49.00

AMS Member Price: $39.20

MAA Member Price: $44.10

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#### Supplemental Materials

# \(p\)-adic Geometry: Lectures from the 2007 Arizona Winter School

Share this page *Editors and Authors: *
*David Savitt; Dinesh S. Thakur; Matthew Baker; Brian Conrad; Samit Dasgupta; Kiran S. Kedlaya; Jeremy Teitelbaum*

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

# Table of Contents

## $p$-adic Geometry: Lectures from the 2007 Arizona Winter School

- Cover Cover11 free
- Title page iii5 free
- Contents v8 free
- Preface vii10 free
- Foreword ix12 free
- Non-archimedean analytic geometry: first steps 116 free
- Several approaches to non-archimedean geometry 924
- The 𝑝-adic upper half plane 6580
- An introduction to Berkovich analytic spaces and non-archimedean potential theory on curves 123138
- 𝑝-adic cohomology: from theory to practice 175190
- Back Cover Back Cover1220