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Class Field Theory / by Nancy Childress

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Universitext | SpringerLink BücherPublisher: New York, NY : Springer-Verlag New York, 2009Description: Online-Ressource (XII, 324p. 25 illus, digital)ISBN:
  • 9780387724904
  • 1281850888
  • 9781281850881
Subject(s): Additional physical formats: 9780387724898 | Buchausg. u.d.T.: Class field theory. New York, NY : Springer, 2009. X, 226 S.DDC classification:
  • 512.7/4
  • 512.3 23
  • 512.74
MSC: MSC: *11-01 | 11R37RVK: RVK: SK 180LOC classification:
  • QA247
DOI: DOI: 10.1007/978-0-387-72490-4Online resources: Summary: A Brief Review -- Dirichlet#x2019;s Theorem on Primes in Arithmetic Progressions -- Ray Class Groups -- The Id#x00E8;lic Theory -- Artin Reciprocity -- The Existence Theorem, Consequences and Applications -- Local Class Field Theory.Summary: 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.PPN: PPN: 1647561124Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
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