Advertisement

Elliptic Curves

  • Dale Husemöller

Part of the Graduate Texts in Mathematics book series (GTM, volume 111)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Dale Husemöller
    Pages 43-61
  3. Dale Husemöller
    Pages 62-80
  4. Dale Husemöller
    Pages 99-119
  5. Dale Husemöller
    Pages 120-137
  6. Dale Husemöller
    Pages 152-161
  7. Dale Husemöller
    Pages 162-182
  8. Dale Husemöller
    Pages 183-201
  9. Dale Husemöller
    Pages 202-221
  10. Dale Husemöller
    Pages 222-241
  11. Dale Husemöller
    Pages 242-261
  12. Dale Husemöller
    Pages 262-271
  13. Back Matter
    Pages 315-350

About this book

Introduction

This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer.

This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory.

About the First Edition:

"All in all the book is well written, and can serve as basis for a student seminar on the subject."

-G. Faltings, Zentralblatt

Keywords

Finite Forth Galois theory Grad Hypergeometric function Natural algebraic curve complex analysis elliptic curve form presentation proof recording theorem theta function

Authors and affiliations

  • Dale Husemöller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-5119-2
  • Copyright Information Springer-Verlag New York 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-5121-5
  • Online ISBN 978-1-4757-5119-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site