LMSST: 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts, Series Number 24) - Hardcover

Cassels, J. W. S.

Hardcover

ISBN 10: 0521415179 ISBN 13: 9780521415170

Publisher: Cambridge University Press, 1991

Synopsis

The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.

About this title

Review

'... an excellent introduction ... written with humour.' Monatshefte für Mathematik

Edition details

• Publisher: Cambridge University Press
• Publication date: 1991
• ISBN 10: 0521415179
• ISBN 13: 9780521415170
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 143