Elliptic Curves

• Main Author: Husem©œller, Dale. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2004.
• Edition: Second Edition.
• Series: Graduate Texts in Mathematics, 111
• Subjects: Mathematics.; Algebraic geometry.; Algebraic Geometry.
• Online Access: View fulltext via EzAccess

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...

Table of Contents:

• to Rational Points on Plane Curves
• Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve
• Plane Algebraic Curves
• Elliptic Curves and Their Isomorphisms
• Families of Elliptic Curves and Geometric Properties of Torsion Points
• Reduction mod p and Torsion Points
• Proof of MordellỚ"s Finite Generation Theorem
• Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields
• Descent and Galois Cohomology
• Elliptic and Hypergeometric Functions
• Theta Functions
• Modular Functions
• Endomorphisms of Elliptic Curves
• Elliptic Curves over Finite Fields
• Elliptic Curves over Local Fields
• Elliptic Curves over Global Fields and ?-Adic Representations
• L-Function of an Elliptic Curve and Its Analytic Continuation
• Remarks on the Birch and Swinnerton-Dyer Conjecture
• Remarks on the Modular Elliptic Curves Conjecture and FermatỚ"s Last Theorem
• Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties
• Families of Elliptic Curves.