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Advanced Topics in the Arithmetic of Elliptic Curves

  • Textbook
  • © 1994

Overview

Authors:
  1. Joseph H. Silverman

    1. Mathematics Department, Brown University, Providence, USA

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Joseph H. Silverman
    Pages 1-4

  3. Elliptic and Modular Functions

    • Joseph H. Silverman
    Pages 5-94

  4. Complex Multiplication

    • Joseph H. Silverman
    Pages 95-186

  5. Elliptic Surfaces

    • Joseph H. Silverman
    Pages 187-288

  6. The Néron Model

    • Joseph H. Silverman
    Pages 289-407

  7. Elliptic Curves over Complete Fields

    • Joseph H. Silverman
    Pages 408-453

  8. Local Height Functions

    • Joseph H. Silverman
    Pages 454-480

  9. Back Matter

    Pages 481-528
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematics Department, Brown University, Providence, USA

    Joseph H. Silverman

Bibliographic Information

  • Book Title: Advanced Topics in the Arithmetic of Elliptic Curves

  • Authors: Joseph H. Silverman

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0851-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94325-1Published: 04 November 1994

  • Softcover ISBN: 978-0-387-94328-2Published: 04 November 1994

  • eBook ISBN: 978-1-4612-0851-8Published: 01 December 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIII, 528

  • Topics: Algebraic Geometry, Number Theory

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