Lectures on Elliptic Curves (London Mathematical Society

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Lectures on Elliptic Curves (London Mathematical Society Student Texts, Vol. 24)
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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 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.
Country USA
Brand Cambridge University Press
Manufacturer Cambridge University Press
Binding Paperback
ItemPartNumber 5 b/w illus.
Color Blue
UnitCount 1
Format Illustrated
EANs 9780521425308
ReleaseDate 0000-00-00

Country	USA
Brand	Cambridge University Press
Manufacturer	Cambridge University Press
Binding	Paperback
ItemPartNumber	5 b/w illus.
Color	Blue
UnitCount	1
Format	Illustrated
EANs	9780521425308
ReleaseDate	0000-00-00

Lectures on Elliptic Curves (London Mathematical Society Student Texts, Vol. 24)

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