ENGLISH

The Arithmetic of Elliptic Curves

By Joseph H. Silverman

Book information

Publisher
Springer
Year
2009
ISBN
0387094938, 9780387094939
Language
english
Format
PDF
Filesize
6 MB (6237547 bytes)
Series
Graduate Texts in Mathematics, 106
Edition
2
Pages
533\521
Time added
2023-02-03 20:48:05

Description

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.

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