The Arithmetic of Elliptic Curves

The Arithmetic of Elliptic Curves by Joseph H. Silverman.

The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently b...

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Bibliographic Details
Main Author: Silverman, Joseph H. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1986.
Edition:1st ed. 1986.
Series:Graduate Texts in Mathematics, 106
Springer eBook Collection.
Subjects:
Algebra.
Number theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I Algebraic Varieties
  • II Algebraic Curves
  • III The Geometry of Elliptic Curves
  • IV The Formal Group of an Elliptic Curve
  • V Elliptic Curves over Finite Fields
  • VIElliptic Curves over ?
  • VII Elliptic Curves over Local Fields
  • VIII Elliptic Curves over Global Fields
  • IX Integral Points on Elliptic Curves
  • X Computing the Mordell-Weil Group
  • Appendix A Elliptic Curves in Characteristics 2 and 3
  • §1. Cohomology of Finite Groups
  • §2. Galois Cohomology
  • §3. Non-Abelian Cohomology
  • Appendix C Further Topics: An Overview
  • §11. Complex Multiplication
  • §12. Modular Functions
  • §13. Modular Curves
  • §14. Tate Curves
  • §15. Néron Models and Tate’s Algorithm
  • §17. Duality Theory
  • §18. Local Height Functions
  • §19. The Image of Galois
  • §20. Function Fields and Specialization Theorems
  • Notes on Exercises
  • List of Notation.

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