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Author : A. Borel
Publisher : Springer
ISBN 13 : 3540347984
Total Pages : 110 pages
Book Rating : 4.5/5 (43 download)
Download or read book Seminar on Complex Multiplication written by A. Borel and published by Springer. This book was released on 2007-08-16 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seminar on Complex Multiplication written by and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Borel
Publisher :
ISBN 13 : 9783662173909
Total Pages : 112 pages
Book Rating : 4.1/5 (739 download)
Download or read book Seminar on Complex Multiplication written by A. Borel and published by . This book was released on 2014-09-01 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : 102 pages
Book Rating : 4.:/5 (66 download)
Download or read book Seminar on Complex Multiplication written by Armand Borel and published by . This book was released on 1966 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Horvath
Publisher : Springer
ISBN 13 : 3540364935
Total Pages : 297 pages
Book Rating : 4.5/5 (43 download)
Download or read book Several Complex Variables. Maryland 1970. Proceedings of the International Mathematical Conference, Held at College Park, April 6-17, 1970 written by John Horvath and published by Springer. This book was released on 2006-11-15 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David A. Cox
Publisher : American Mathematical Soc.
ISBN 13 : 1470470284
Total Pages : 551 pages
Book Rating : 4.4/5 (74 download)
Download or read book Primes of the Form x2+ny2 : Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions written by David A. Cox and published by American Mathematical Soc.. This book was released on 2022-11-16 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies when a prime p can be written in the form x2+ny2. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of p=x2+ny2. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields. The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics.
Author : Robert M. Brooks
Publisher : Springer
ISBN 13 : 3540364552
Total Pages : 244 pages
Book Rating : 4.5/5 (43 download)
Download or read book Symposium on Several Complex Variables. Park City, Utah, 1970 written by Robert M. Brooks and published by Springer. This book was released on 2006-11-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles based on talks given at the Symposium on several complex variables, Park City, March 30 - April 3, 1970. The papers herein represent a broad spectrum of mathematical research (e.g. function algebras, sheaf theory, differential operators, manifolds) but are related by the fact that they are all related to some degree to the area of several complex variables.
Author : David V. Chudnovsky
Publisher : Springer Science & Business Media
ISBN 13 : 1475741588
Total Pages : 279 pages
Book Rating : 4.4/5 (757 download)
Download or read book Number Theory written by David V. Chudnovsky and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: New York Number Theory Seminar started its regular meeting in January, 1982. The Seminar has been meeting on a regular basis weekly during the academic year since then. The meeting place of the seminar is in midtown Manhattan at the Graduate School and University Center of the City Uni versity of New York. This central location allows number-theorists in the New York metropolitan area and vistors an easy access. Four volumes of the Seminar proceedings, containing expanded texts of Seminar's lectures had been published in the Springer's Lecture Notes in Mathematics series as volumes 1052 (1984), 1135 (1985), 1240 (1987), and 1383 (1989). Seminar co chairmen are pleased that some of the contributions to the Seminar opened new avenues of research in Number Theory and related areas. On a histori cal note, one of such contributions proved to be a contribution by P. Landweber. In addition to classical and modern Number Theory, this Semi nar encourages Computational Number Theory. This book presents a selection of invited lectures presented at the New York Number Theory Seminar during 1989-1990. These papers cover wide areas of Number Theory, particularly modular functions, Aigebraic and Diophantine Geometry, and Computational Number Theory. The review of C-L. Chai presents a broad view of the moduli of Abelian varieties based on recent work of the author and many other prominent experts. This provides the reader interested in Diophantine Analysis with access to state of the art research. The paper of D. V. and G. V.
Author : Christian Rohde
Publisher : Springer Science & Business Media
ISBN 13 : 3642006388
Total Pages : 234 pages
Book Rating : 4.6/5 (42 download)
Download or read book Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication written by Christian Rohde and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1989-06 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ching-Li Chai
Publisher : American Mathematical Soc.
ISBN 13 : 1470410141
Total Pages : 402 pages
Book Rating : 4.4/5 (74 download)
Download or read book Complex Multiplication and Lifting Problems written by Ching-Li Chai and published by American Mathematical Soc.. This book was released on 2013-12-19 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry.
Author : R. V. Gamkrelidze
Publisher : Springer Science & Business Media
ISBN 13 : 1468433067
Total Pages : 258 pages
Book Rating : 4.4/5 (684 download)
Download or read book Progress in Mathematics written by R. V. Gamkrelidze and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains five review articles, two in the Algebra part and three in the Geometry part, surveying the fields of cate gories and class field theory, in the Algebra part, and of Finsler spaces, structures on differentiable manifolds, and packing, cover ing, etc., in the Geometry part. The literature covered is primar Hy that published in 1964-1967. Contents ALGEBRA CATEGORIES ............... . 3 M. S. Tsalenko and E. G. Shul'geifer § 1. Introduction........... 3 § 2. Foundations of the Theory of Categories . . . . . 4 § 3. Fundamentals of the Theory of Categories . . . . . 6 § 4. Embeddings of Categories ... . . . . . . . . . . . . 14 § 5. Representations of Categories . . . . . . . . . . . . . 16 § 6. Axiomatic Characteristics of Algebraic Categories . . . . . . . . . . . . . . . . . . . . . . . . . . 18 § 7. Reflective Subcategories; Varieties. . . 20 § 8. Radicals in Categories . . . . . . . 24 § 9. Categories with Involution. . . . . . 29 § 10. Universal Algebras in Categories . 30 § 11. Categories with Multiplication . . . 34 § 12. Duality of Functors. .. ....... 37 § 13. Homotopy Theory . . . . .. ........... 39 § 14. Homological Algebra in Categories. . . . . . 41 § 15. Concrete Categories . . . . .. ......... 44 § 16. Generalizations.. . . . . . . 45 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 CLASS FIELD THEORY. FIELD EXTENSIONS. . . . . . . . 59 S. P. Demushkin 66 Literature Cited vii CONTENTS viii GEOMETRY 75 FINSLER SPACES AND THEIR GENERALIZATIONS ..
Author : Ehud De Shalit
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.4/5 (91 download)
Download or read book Iwasawa Theory of Elliptic Curves with Complex Multiplication written by Ehud De Shalit and published by . This book was released on 1987 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David A. Cox
Publisher : John Wiley & Sons
ISBN 13 : 1118031008
Total Pages : 372 pages
Book Rating : 4.1/5 (18 download)
Download or read book Primes of the Form x2 + ny2 written by David A. Cox and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
Author : J. L. Morris
Publisher : Springer
ISBN 13 : 3540361588
Total Pages : 283 pages
Book Rating : 4.5/5 (43 download)
Download or read book Conference on the Numerical Solution of Differential Equations written by J. L. Morris and published by Springer. This book was released on 2006-11-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P.J. Hilton
Publisher : Springer
ISBN 13 : 3540361405
Total Pages : 498 pages
Book Rating : 4.5/5 (43 download)
Download or read book Category Theory, Homology Theory and Their Applications. Proceedings of the Conference Held at the Seattle Research of the Battelle Memorial Institute, June 24 - July 19, 1968 written by P.J. Hilton and published by Springer. This book was released on 2006-11-14 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. J. Hilton
Publisher : Springer
ISBN 13 : 3540360956
Total Pages : 227 pages
Book Rating : 4.5/5 (43 download)
Download or read book Category Theory, Homology Theory and Their Applications. Proceedings of the Conference Held at the Seattle Research Center of the Battelle Memorial Institute, June 24 - July 19, 1968 written by P. J. Hilton and published by Springer. This book was released on 2006-11-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:
