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Titlebook: Complex Multiplication; Serge Lang Book 1983 Springer-Verlag New York Inc. 1983 Abelian varieties.Abelian variety.Finite.Komplexe Multipli

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书目名称Complex Multiplication
编辑Serge Lang
视频video
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Complex Multiplication;  Serge Lang Book 1983 Springer-Verlag New York Inc. 1983 Abelian varieties.Abelian variety.Finite.Komplexe Multipli
描述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 C
出版日期Book 1983
关键词Abelian varieties; Abelian variety; Finite; Komplexe Multiplikation; algebra; congruence; construction; ell
版次1
doihttps://doi.org/10.1007/978-1-4612-5485-0
isbn_softcover978-1-4612-5487-4
isbn_ebook978-1-4612-5485-0Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag New York Inc. 1983
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Some Algebraic Properties of Abelian Varieties, situation, and we assume that the reader is acquainted with the general theory of abelian varieties. No matter whether the reader picks up the basic properties from my book on the subject (after Weil), Mumford, Shimura (for reduction mod .), or the foundations laid by the Grothendieck school, the r
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Algebraic Complex Multiplication,then the Frobenius endomorphism of the variety mod . can be represented as the reduction mod p of an element in that ring, which is, say, the ring of integers in a number field K. If π is that element, then a basic theorem gives the ideal factorization of π in .. We have followed Shimura-Taniyama fo
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Case Study: Control of Navigable Rivers,s. Let . be a vector space of dimension . over the complex numbers. Let Λ be a lattice in .. The quotient complex analytic group ./Λ is called a .. We assume known the basic facts concerning Riemann forms and the projective embedding of such toruses. A (non-degenerate) . . on ./Λ is an alternating n
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