The Arithmetic of Elliptic Curves / Edition 2

The Arithmetic of Elliptic Curves / Edition 2

by Joseph H. Silverman
     
 

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ISBN-10: 1441918582

ISBN-13: 9781441918581

Pub. Date: 11/19/2010

Publisher: Springer New York

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds

Overview

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Product Details

ISBN-13:
9781441918581
Publisher:
Springer New York
Publication date:
11/19/2010
Series:
Graduate Texts in Mathematics Series, #106
Edition description:
Softcover reprint of hardcover 2nd ed. 2009
Pages:
513
Product dimensions:
6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell#x2013;Weil Group.- Algorithmic Aspects of Elliptic Curves.

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