The Arithmetic of Elliptic Curves

Joseph H. Silverman - Collection Graduate Texts in Mathematics

410 pages, parution le 03/06/2005

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Résumé

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.

Written for: math grad stud mathematicians

Sommaire

Algebraic Varieties
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-Weil Group
Appendices

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Joseph H. Silverman
Collection	Graduate Texts in Mathematics
Parution	03/06/2005
Nb. de pages	410
Format	16 x 24
Couverture	Relié
Poids	715g
Intérieur	Noir et Blanc
EAN13	9780387962030
ISBN13	978-0-387-96203-0