Class Field Theory
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Introduction To Non Abelian Class Field Theory An Automorphic Forms Of Weight 1 And 2 Dimensional Galois Representations
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Author : Toyokazu Hiramatsu
language : en
Publisher: World Scientific
Release Date : 2016-09-13
Introduction To Non Abelian Class Field Theory An Automorphic Forms Of Weight 1 And 2 Dimensional Galois Representations written by Toyokazu Hiramatsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-13 with Mathematics categories.
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.
Class Field Theory
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Author : Emil Artin
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Class Field Theory written by Emil Artin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory ... In this revised edition, two mathematical additions complementing the exposition of the original text are made. The new edition also contains several new footnotes, additional references, and historical comments.
Class Field Theory
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Author : Nancy Childress
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Class Field Theory written by Nancy Childress and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-28 with Mathematics categories.
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.
Local Class Field Theory
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Author : Kenkichi Iwasawa
language : en
Publisher: Oxford University Press, USA
Release Date : 1986
Local Class Field Theory written by Kenkichi Iwasawa and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with History categories.
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.
Introduction To The Construction Of Class Fields
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Author : Harvey Cohn
language : en
Publisher: CUP Archive
Release Date : 1985-08-30
Introduction To The Construction Of Class Fields written by Harvey Cohn and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08-30 with Mathematics categories.
In this graduate level textbook, Professor Cohn takes a problem that Pythagoras could have posed, and using it as motivation, develops a constructional introduction to classical field theory and modular function theory. The interest in constructional techniques has increased recently with the advent of cheap and plentiful computer technology. The beginning chapters provide the motivation and necessary background in elementary algebraic number theory and Riemann surface theory. The ideas and results are then applied and extended to class field theory. In the later chapters, more specialized results are presented, with full proofs, though the author emphasizes, with examples, the relation of the material to other parts of mathematics.
Class Field Theory
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Author : Georges Gras
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-16
Class Field Theory written by Georges Gras and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-16 with Mathematics categories.
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.
Class Field Theory
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Author : Jürgen Neukirch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-08
Class Field Theory written by Jürgen Neukirch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Mathematics categories.
The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields.
Class Field Theory
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Author : Claude Chevalley
language : en
Publisher:
Release Date : 1954
Class Field Theory written by Claude Chevalley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Mathematics categories.
Class Field Theory
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Author : J. Neukirch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Class Field Theory written by J. Neukirch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol ogy, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group theoretical principle, admitting an entirely elementary description. This de scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here.
Class Field Theory Proofs And Applications
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Author : Daniel Fretwell
language : en
Publisher: GRIN Verlag
Release Date : 2011-07-27
Class Field Theory Proofs And Applications written by Daniel Fretwell and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-27 with Mathematics categories.
Research Paper (postgraduate) from the year 2011 in the subject Mathematics - Number Theory, grade: Postgraduate, University of Sheffield, language: English, abstract: This document is a continuation of my Semester 1 project on class field theory. In the previous work, we made a rounded exposition of the fundamentals of class field theory but in order to preserve the document length the main proofs had to be skipped. We concentrate on filling in the gaps in this second installment. Due to the need to complete the arguments left open last semester and the need for applications this part of the project is a little longer than it should have been. It was not mentioned in the previous project but the class field theory we are studying here is global class field theory. There is such a thing as local class field theory in which we study the Abelian extensions of local fields (essentially fields that arise as completions of a number field with respect to places). Actually we touch on these ideas slightly in this project but never quite get to de_ning a local Artin map and looking at the local analogues of the main theorems of global class field theory. For those wanting to continue on to study local class field theory, consider Chapter 7 of [2] To start off this project we shall first restate the main de_nitions and theorems. This will be brief and those wanting to remind themselves of the details should consult my Semester 1 project. There will be very little motivation or technical results here since this was the purpose of the work done previously. We then set out to prove the main theorems of class field theory. With our present knowledge this would not be a simple task and we soon find that we first have to invent or discover new concepts such as the idele group and the corresponding idele class group. These are topological devices that take stock of all completions of a number eld at once. Such constructions will make the theory much easier to understand and formulate, whilst at the same time generalising the theory to all Abelian extensions. The cohomology of nite Abelian groups will be introduced and used alongside the idele theory to establish an important inequality. We use L-series in conjunction with the ideal theory to establish another important inequality. Combining the two inequalities will give a nice result that allows us to prove Artin reciprocity. In order to prove the existence theorem we resort to using Kummer n-extensions and the notion of a class eld. This middle chunk of the project will be quite technical but hopefully enjoyable and illuminating. [...]