**IAS/Park City Mathematics Series**

Volume: 9;
2001;
569 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-4448-9

Product Code: PCMS/9.S

List Price: $88.00

Individual Member Price: $70.40

**Electronic ISBN: 978-1-4704-3908-8
Product Code: PCMS/9.E**

List Price: $88.00

Individual Member Price: $70.40

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# Arithmetic Algebraic Geometry

Share this page *Edited by *
*Brian Conrad; Karl Rubin*

A co-publication of the AMS and IAS/Park City Mathematics Institute

The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

Titles in this series are co-published with the Institute
for Advanced Study/Park City Mathematics Institute. Members of the
Mathematical Association of America (MAA) and the National Council of
Teachers of Mathematics (NCTM) receive a 20% discount from list
price. *NOTE: This discount does not apply to volumes in this
series co-published with the Society for Industrial and Applied
Mathematics (SIAM).*

#### Readership

Graduate students and research mathematicians interested in arithmetic algebraic geometry.

#### Reviews & Endorsements

The book … gives a good overview of the subject and proceeds naturally to more technical aspects of the theory. An attractive feature of the book is the presence of many exercises for students.

-- European Mathematical Society Newsletter

#### Table of Contents

# Table of Contents

## Arithmetic Algebraic Geometry

- Cover Cover11
- Title page iii4
- Contents v6
- Preface xiii14
- Introduction 116
- Elliptic curves, modular forms, and applications 520
- Open questions in arithmetic algebraic geometry 8398
- Lectures on Serre’s conjectures 143158
- Deformations of Galois representations 233248
- Introduction to Iwasawa theory for elliptic curves 407422
- Galois cohomology 465480
- The arithmetic of modular forms 481496
- Arithmetic of certain Calabi-Yau varieties and mirror symmetry 507522
- Back Cover Back Cover1585