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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Complex Multiplication

Complex Multiplication

Lang, S.

Paperback

Series: Grundlehren Der Mathematischen Wissenschaften, Book 255

AlgebraGeneral Mathematics

ISBN10: 1461254876
ISBN13: 9781461254874
Publisher: Springer Nature
Published: Oct 31 2011
Pages: 184
Weight: 0.62
Height: 0.42 Width: 6.14 Depth: 9.21
Language: English
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 Chapter6 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 . . . . .

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