Graduate Texts in Mathematics

Silverman, Joseph H.

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 theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel’s theorem and explicit computations for the curve Y^2 = X^3 + DX.

Details

Published by: Springer

Publication Date: 2009-05-29

Format: Hardcover

ISBN-13: 9780387094939

DOI: 10.1007/978-0-387-09494-6

Dimensions: 235cm x155cm

Pages: 513