Lectures on Elliptic Curves pdf epub mobi txt 电子书 下载 2024


Lectures on Elliptic Curves

简体网页||繁体网页
J. W. S. Cassels
Cambridge University Press
1991-11-21
144
GBP 19.99
Paperback
London Mathematical Society Student Texts
9780521425308

图书标签: 椭圆曲线  数论  数学  Cassels  on  Lectures  LMSST  Elliptic   


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发表于2024-11-07

Lectures on Elliptic Curves epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Lectures on Elliptic Curves epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Lectures on Elliptic Curves pdf epub mobi txt 电子书 下载 2024



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The study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is 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-Weil 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, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text.

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