2 edition of **Complex multiplication of Abelian varieties and its applications to number theory** found in the catalog.

Complex multiplication of Abelian varieties and its applications to number theory

GorЕЌ Shimura

- 184 Want to read
- 6 Currently reading

Published
**1961**
by Mathematical Society of Japan in [Tokyo]
.

Written in English

- Abelian varieties.,
- Number theory.

**Edition Notes**

Bibliography: p. 152-154.

Statement | by Goro Shimura and ... Yutaka Taniyama. |

Series | Publications of the Mathematical Society of Japan ;, 6 |

Contributions | Taniyama, Yutaka, joint author. |

Classifications | |
---|---|

LC Classifications | QA241 .S45 |

The Physical Object | |

Pagination | xi, 159 p. |

Number of Pages | 159 |

ID Numbers | |

Open Library | OL220339M |

LC Control Number | a 61005716 |

Frontmatter --Contents --Preface --Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory () --Notation and Terminology --I. Preliminaries on Abelian Varieties --II. Abelian Varieties with Complex Multiplication --III. Reduction of Constant Fields --IV. Construction of Class Fields --V. The starting point of this Lecture Notes volume is Deligne's theorem about absolute Hodge cycles on abelian varieties. Its applications to the theory of motives with complex multiplication are systematically reviewed. In particular, algebraic relations between values .

Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory () --Ch. I. Preliminaries on Abelian Varieties --Ch. II. Abelian Varieties with Complex Multiplication --Ch. III. Reduction of Constant Fields - . Complex multiplication of abelian varieties and its applications to number theory. Publications of the Mathematical Society of Japan, 6 The Mathematical Society of Japan, Tokyo xi+ pp. MR Shimura, Goro. Introduction to the arithmetic theory of automorphic functions. Kanô Memorial Lectures, No. 1.

The starting point of this Lecture Notes volume is Deligne's theorem about absolute Hodge cycles on abelian varieties. Its applications to the theory of motives with complex multiplication are systematically reviewed. G. SHIMURA AND Y. TANIYAMA, "Complex Multiplication of Abelian Varieties and Its Applications to Number Theory," Publ. Math. Soc. Japan No. 6, 5. H. YOSHIDA, Abelian varieties with complex multiplication and representations of the Weil groups, Ann. of Math. (), Cited by: 2.

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Complex multiplication of Abelian varieties and its applications to number theory, (Publications of the Mathematical Society of Japan) Paperback – January 1, by Goro Shimura (Author), Yutaka Taniyama (Author)Price: $ "[This book] is a beautifully written, self-contained and complete treatment of a subject of which G.

Shimura is a founding master, and is a fundamental reference for any researcher or student of the antimetric theory of abelian varieties and modular functions, and in particular of its applications to class field theory.", Bulletin of the Cited by: Complex multiplication of Abelian varieties and its applications to number theory.

[Tokyo] Mathematical Society of Japan, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors. "[This book] is a beautifully written, self-contained and complete treatment of a subject of which G. Shimura is a founding master, and is a fundamental reference for any researcher or student of the antimetric theory of abelian varieties and modular functions, and in particular of its applications to class field theory.", Bulletin of the Manufacturer: Princeton University Press.

Complex multiplication of Abelian varieties and its applications to number theory Volume 6 of Publications of the Mathematical Society of Japan, Nihon-Sūgakkai Volume 6 of Publications (Nihon Sūgakkai) Authors: Gorō Shimura, Yutaka Taniyama: Publisher: Mathematical Society of Japan, Original from: the University of Michigan: Digitized.

Get this from a library. Complex multiplication of abelian varieties and its applications to number theory. [Gorō Shimura; Yutaka Taniyama]. "[This book] is a beautifully written, self-contained and complete treatment of a subject of which G.

Shimura is a founding master, and is a fundamental reference for any researcher or student of the antimetric theory of abelian varieties and modular functions, and in particular of its applications to class field theory.".

Abelian varieties with complex multiplication and modular functions Goro Shimura. Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions.

In Hilbert proposed the generalization of. Jacobians with complex multiplication. Abstract. In this paper we will say that a simple abelian variety X is of CM type if there is a number field K with [K: Q] = 2 dim(X) such that K ⊂ End°(X). If X is any abelian variety, then we will say that X is of CM type if all its simple factors by: going to focus on the theory of complex multiplication of abelian varieties, the main goal being the proof of the main theorem of complex multiplication over the re ex eld.

It describes how an abelian variety with complex multiplication behaves under the action of an automorphism ˙ of C xing a eld called the re ex Size: KB. The aim of §§ is to complement the theory of reduction modulo $\mathfrak{p}$ of algebraic varieties, given in [33], with a particular interest in abelian varieties, toward the later use.

We will first recall definitions and results from the general theory with a slight modification, and then proceed to the main subject. This would be a vague question, but I still want to ask here.

Do you have any recommended book on complex multiplicaton. I know only 2 books: Shimura's book Abelian Varieties with Complex Multiplication and Modular Functions and Lang's book Complex a's book used old-language (published in ), and I feel it would be nice to read this book when I.

Complex multiplication of abelian varieties. In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for elliptic curves in the nineteenth century.

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions.

A similar theory can be developed for Price: $ Abelian Varieties with Complex Multiplication and Modular Functions (Princeton Mathematical Series Book 46) - Kindle edition by Shimura, Goro. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading Abelian Varieties with Complex Multiplication and Modular Functions (Princeton Mathematical Series Book Manufacturer: Princeton University Press. Shimura, Goro; Taniyama, Yutaka (), Complex multiplication of abelian varieties and its applications to number theory, Publications of the Mathematical Society of Japan, 6, Tokyo: The Mathematical Society of Japan, MR Later expanded and published as Shimura () Shimura, Goro ().

Automorphic Functions and Number : Guggenheim Fellowship (), Cole Prize. G. SHIMURA and T. TANIYAMA- Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Jap., 6 ().Cited by: Series on Number Theory and Its Applications Number Theory: Plowing and Starring Through High Wave Forms, pp.

() No Access COMPLEX MULTIPLICATION IN THE SENSE OF ABEL KATSUYA MIYAKE. abelian varieties 95 [12] G. Shimura, Construction of class elds and zeta functions algebraic curves, Ann. of Math., 85 (), [13] G.

Shimura and Y. Taniyama, Complex multiplication abelian of varieties and its applications to number theory, Publ. Math. Soc. Japan, No. 6, Tokyo, [14] Y. Taniyama, Jacobian varieties and number File Size: 1MB. This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language.

The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture.

" far more readable than most it is also. G. Shimura and Y. Taniyama: Complex multiplication of Abelian Varieties and its applications to number theory, Publ.

Math. Soc. Japan, 6(). Google Scholar [14]Cited by: 4.The theory of abelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi.

The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language.Abelian Varieties With Complex Multiplication and Modular Functions, by Shimura, Goro.

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions.

In Hilbert proposed the.