S. Lang Complex Multiplication 9780387907864

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Автор: S. Lang
Название: Complex Multiplication
ISBN: 9780387907864
Издательство: Springer
Классификация:

Теория чисел

ISBN-10: 0387907866
Обложка/Формат: Hardcover
Страницы: 184
Вес: 0.45 кг.
Дата издания: 29.08.1983
Серия: Grundlehren der mathematischen Wissenschaften
Язык: English
Размер: 234 x 156 x 13
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The small book by Shimura-Taniyama on the subject of complex multi- is a classic. It gives the results obtained by them (and some by Weil) plication in the higher dimensional case, generalizing in a non-trivial way the method of Deuring for elliptic curves, by reduction mod p. Partly through the work of Shimura himself (cf. Sh 1] Sh 2], and Sh 5]), and some others (Serre, Tate, Kubota, Ribet, Deligne etc.) it is possible today to make a more snappy and extensive presentation of the fundamental results than was possible in 1961. Several persons have found my lecture notes on this subject useful to them, and so I have decided to publish this short book to make them more widely available. Readers acquainted with the standard theory of abelian varieties, and who wish to get rapidly an idea of the fundamental facts of complex multi- plication, are advised to look first at the two main theorems, Chapter 3, 6 and Chapter 4, 1, as well as the rest of Chapter 4. The applications of Chapter 6 could also be profitably read early. I am much indebted to N. Schappacher for a careful reading of the manu- script resulting in a number of useful suggestions. S. LANG Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive Definite Involutions . . . 6 2. CM Types and Subfields. . . . . 8 3. Application to Abelian Manifolds. 4. Construction of Abelian Manifolds with CM 14 21 5. Reflex of a CM Type . . . . .

Complex Multiplication, S. Lang