An Introduction To Non Abelian Class Field Theory

Author : Toyokazu Hiramatsu
Publisher : World Scientific
ISBN 13 : 9813142286
Total Pages : 188 pages
Book Rating : 4.82/5 ( download)

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Download or read book Introduction To Non-abelian Class Field Theory, An: Automorphic Forms Of Weight 1 And 2-dimensional Galois Representations written by Toyokazu Hiramatsu and published by World Scientific. This book was released on 2016-09-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.

Author : Toyokazu Hiramatsu
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813142268
Total Pages : 175 pages
Book Rating : 4.6X/5 ( download)

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Download or read book An Introduction to Non-Abelian Class Field Theory written by Toyokazu Hiramatsu and published by World Scientific Publishing Company. This book was released on 2017 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.

Author : Toyokazu Hiramatsu
Publisher :
ISBN 13 : 9789813142275
Total Pages : 175 pages
Book Rating : 4.78/5 ( download)

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Download or read book An Introduction to Non-Abelian Class Field Theory written by Toyokazu Hiramatsu and published by . This book was released on 2016 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1."--Publisher's website.

Author : Nancy Childress
Publisher : Springer Science & Business Media
ISBN 13 : 0387724907
Total Pages : 230 pages
Book Rating : 4.04/5 ( download)

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Download or read book Class Field Theory written by Nancy Childress and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof, but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included lots of challenging exercises throughout the text.

Author : Georges Gras
Publisher : Springer Science & Business Media
ISBN 13 : 3662113236
Total Pages : 517 pages
Book Rating : 4.33/5 ( download)

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Download or read book Class Field Theory written by Georges Gras and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

Author : Kenkichi Iwasawa
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.40/5 ( download)

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Download or read book Local Class Field Theory written by Kenkichi Iwasawa and published by Oxford University Press, USA. This book was released on 1986 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This readable introduction to local class field theory, a theory of algebraic extensions, covers such topics as abelian extensions. Almost self-contained, the book is accessible to any reader with a basic background in algebra and topological groups.

Author : Katsuya Miyake
Publisher :
ISBN 13 :
Total Pages : 658 pages
Book Rating : 4.89/5 ( download)

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Download or read book Class Field Theory written by Katsuya Miyake and published by . This book was released on 2001 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles contributed by the speakers at the Mathematical Society of Japan's Seventh International Research Institute entitled, ``Class Field Theory-Its Centenary and Prospect'', held in Tokyo in June 1998. Some of the articles are expository; they discuss important interesting aspects of class field theory and contain full references. Other articles are historical; they vividly explain how leading number theorists in Europe and Japan developed and exchanged their mathematical ideas.

Author : Pierre Guillot
Publisher : Cambridge University Press
ISBN 13 : 1108386261
Total Pages : 309 pages
Book Rating : 4.65/5 ( download)

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Download or read book A Gentle Course in Local Class Field Theory written by Pierre Guillot and published by Cambridge University Press. This book was released on 2018-11-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker–Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.

Author : Emil Artin
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.84/5 ( download)

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Download or read book Class Field Theory written by Emil Artin and published by . This book was released on 1967 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Source Wikipedia
Publisher : University-Press.org
ISBN 13 : 9781230493800
Total Pages : 26 pages
Book Rating : 4.08/5 ( download)

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Download or read book Class Field Theory written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Abelian extension, Albert-Brauer-Hasse-Noether theorem, Artin L-function, Artin reciprocity law, Class formation, Complex multiplication, Conductor (class field theory), Galois cohomology, Genus field, Golod-Shafarevich theorem, Grunwald-Wang theorem, Hasse norm theorem, Hilbert class field, Hilbert symbol, Iwasawa theory, Kronecker-Weber theorem, Lafforgue's theorem, Langlands dual, Langlands-Deligne local constant, Local class field theory, Local Fields (book), Local Langlands conjectures, Non-abelian class field theory, Quasi-finite field, Takagi existence theorem, Tate cohomology group, Weil group. Excerpt: In mathematics, a class formation is a topological group acting on a module satisfying certain conditions. Class formations were introduced by Emil Artin and John Tate to organize the various Galois groups and modules that appear in class field theory. A formation is a topological group G together with a topological G-module A on which G acts continuously. A layer E/F of a formation is a pair of open subgroups E, F of G such that F is a finite index subgroup of E. It is called a normal layer if F is a normal subgroup of E, and a cyclic layer if in addition the quotient group is cyclic. If E is a subgroup of G, then A is defined to be the elements of A fixed by E. We write H(E/F)for the Tate cohomology group H(E/F, A) whenever E/F is a normal layer. (Some authors think of E and F as fixed fields rather than subgroup of G, so write F/E instead of E/F.) In applications, G is often the absolute Galois group of a field, and in particular is profinite, and the open subgroups therefore correspond to the finite extensions of the field contained in some fixed separable closure. A class formation is a formation such that for every normal layer E/F H(E/F) is trivial, andH(E/F) is cyclic of order E/F.In...