Advanced Topics in the Arithmetic of Elliptic Curves

  • Joseph H. Silverman

Part of the Graduate Texts in Mathematics book series (GTM, volume 151)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Joseph H. Silverman
    Pages 1-4
  3. Joseph H. Silverman
    Pages 5-94
  4. Joseph H. Silverman
    Pages 95-186
  5. Joseph H. Silverman
    Pages 187-288
  6. Joseph H. Silverman
    Pages 289-407
  7. Joseph H. Silverman
    Pages 408-453
  8. Joseph H. Silverman
    Pages 454-480
  9. Back Matter
    Pages 481-528

About this book

Introduction

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

Keywords

Elliptic Curve algebraic surface arithmetic Divisor elliptic curve modular curve

Authors and affiliations

  • Joseph H. Silverman
    • 1
  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0851-8
  • Copyright Information Springer-Verlag New York, Inc. 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94328-2
  • Online ISBN 978-1-4612-0851-8
  • Series Print ISSN 0072-5285
  • About this book