Class Field Theory

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Universitext

ISBN: 0387724893
ISBN 13: 9780387724898
Autor: Childress, Nancy
Verlag: Springer Verlag GmbH
Umfang: x, 226 S., 30 Fotos
Erscheinungsdatum: 24.11.2008
Auflage: 1/2008
Format: 1.2 x 23.6 x 15.8
Gewicht: 344 g
Produktform: Kartoniert
Einband: KT

Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. Some of its consequences (e.g., the Chebotarev density theorem) apply even to nonabelian extensions.   This book is an accessible introduction to class field theory. It takes a traditional approach in that it presents the global material first, using some of the original techniques of proof, but in a fashion that 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 exercises throughout the text.   Professor Nancy Childress is a member of the Mathematics Faculty at Arizona State University.

Artikelnummer: 1120095 Kategorie:

Beschreibung

Inhaltsverzeichnis

Preface.- A Brief Review.- Dirichlet''s Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Idelic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and Applications.- Local Class Field Theory.- Bibliography.- Index.

Autorenporträt

InhaltsangabeA Brief Review.- Dirichlet’s Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Idèlic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and Applications.- Local Class Field Theory.

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