Class Field Theory
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Class Field Theory
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Author : Georges Gras
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
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 2013-11-11 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 : 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.
Galois Cohomology And Class Field Theory
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Author : David Harari
language : en
Publisher: Springer Nature
Release Date : 2020-06-24
Galois Cohomology And Class Field Theory written by David Harari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-24 with Mathematics categories.
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
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.
Algebraic Groups And Class Fields
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Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Groups And Class Fields written by Jean-Pierre Serre 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.
Translation of the French Edition
A Gentle Course In Local Class Field Theory
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Author : Pierre Guillot
language : en
Publisher: Cambridge University Press
Release Date : 2018-11
A Gentle Course In Local Class Field Theory written by Pierre Guillot and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11 with Mathematics categories.
A self-contained exposition of local class field theory for students in advanced algebra.
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.
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.
Class Field Theory And L Functions
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Author : Franz Halter-Koch
language : en
Publisher: CRC Press
Release Date : 2022-03-13
Class Field Theory And L Functions written by Franz Halter-Koch and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-13 with Mathematics categories.
The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras. While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020). The main features of the book are: A detailed study of Pontrjagin’s dualtiy theorem. A thorough presentation of the cohomology of profinite groups. A introduction to simple algebras. An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language. The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse. The study of holomorphy domains and their relevance for class field theory. Simple classical proofs of the functional equation for L functions both for number fields and function fields. A self-contained presentation of the theorems of representation theory needed for Artin L functions. Application of Artin L functions for arithmetical results.