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Author : Pierre Guillot
Release : 2018-11
Genre : Mathematics
Kind : eBook
Book Rating : 776/5 ( reviews)
Book Synopsis A Gentle Course in Local Class Field Theory by : Pierre Guillot
Download or read book A Gentle Course in Local Class Field Theory written by Pierre Guillot. This book was released on 2018-11. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained exposition of local class field theory for students in advanced algebra.
Author : Jean-Pierre Serre
Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 739/5 ( reviews)
Book Synopsis Local Fields by : Jean-Pierre Serre
Download or read book Local Fields written by Jean-Pierre Serre. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Author : Kenkichi Iwasawa
Release : 1986
Genre : History
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Local Class Field Theory by : Kenkichi Iwasawa
Download or read book Local Class Field Theory written by Kenkichi Iwasawa. This book was released on 1986. 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 : J. Neukirch
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 65X/5 ( reviews)
Book Synopsis Class Field Theory by : J. Neukirch
Download or read book Class Field Theory written by J. Neukirch. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Nancy Childress
Release : 2008-10-28
Genre : Mathematics
Kind : eBook
Book Rating : 907/5 ( reviews)
Book Synopsis Class Field Theory by : Nancy Childress
Download or read book Class Field Theory written by Nancy Childress. This book was released on 2008-10-28. 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.
