Elliptic Curves

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...

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Main Author: Husemoller, Dale
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 1987, 1987
Edition:1st ed. 1987
Series:Graduate Texts in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • to Rational Points on Plane Curves
  • 1 Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve
  • 2 Plane Algebraic Curves
  • 3 Elliptic Curves and Their Isomorphisms
  • 4 Families of Elliptic Curves and Geometric Properties of Torsion Points
  • 5 Reduction mod p and Torsion Points
  • 6 Proof of Mordell’s Finite Generation Theorem
  • 7 Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields
  • 8 Descent and Galois Cohomology
  • 9 Elliptic and Hypergeometric Functions
  • 10 Theta Functions
  • 11 Modular Functions
  • 12 Endomorphisms of Elliptic Curves
  • 13 Elliptic Curves over Finite Fields
  • 14 Elliptic Curves over Local Fields
  • 15 Elliptic Curves over Global Fields and ?-Adic Representations
  • 16 L-Function of an Elliptic Curve and Its Analytic Continuation
  • 17 Remarks on the Birch and Swinnerton-Dyer Conjecture
  • Appendix Guide to the Exercises