Elliptic Curves (Graduate Texts in Math, Vol 111)

Husm, Oller Dale; Husemoller, Dale

ISBN 10: 0387963715 / ISBN 13: 9780387963716

Editore: Springer, 1997

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This book is in Good condition. There may be some notes and highligting but otherwise the book is in overall good condition.

Codice articolo BCV.0387963715.G

Dati bibliografici

• Titolo: Elliptic Curves (Graduate Texts in Math, Vol 111)
• Editore: Springer
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0387963715
• ISBN 13: 9780387963716
• Rilegatura: Rilegato
• Disegnatore: B&W Equations And Diagrams
• Condizione: good

Descrizione articolo

Riassunto

The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven­ tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.

Dalla quarta di copertina

This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer.

This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory.

About the First Edition:

"All in all the book is well written, and can serve as basis for a student seminar on the subject."

-G. Faltings, Zentralblatt