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.
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Book Description
Editorial Reviews
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From the reviews: "The author writes in the preface that the aim of this book is ‘to help in the practical use and understanding of the principles of global class field theory for number fields, without any attempt to give proofs of the foundations …’ . He succeeded in his task admirably. The book brings a huge amount of information on … class field theory, illustrated with many well-chosen examples. … should be an obligatory reading for everybody interested in the modern development of algebraic number theory." (Wladyslaw Narkiewicz, Zentralblatt MATH, Vol. 1019, 2003) "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. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects … . This book … gives much material in an elementary way, and is suitable for students, researchers and all who are fascinated by this theory." (L’Enseignement Mathematique, Vol. 49 (1-2), 2003) "Each subject is treated very clearly from the theoretical side and explained by examples. The richness in examples is among the most attractive features of this book. … The book concludes with a very ample and well-organized bibliography. The writing is very clear and precise throughout. … This book gives an encompassing theoretical picture of large parts of class field theory. It is of particular interest to everybody interested … in this domain. … it is also a very enjoyable book." (Cornelius Greither, Mathematical Reviews, 2003 j)
Language Notes
Text: English (translation)
Original Language: French
Original Language: French
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Inside This Book
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First Sentence:
This chapter gives the definitions of the objects which will be used throughout this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
global reciprocity map, deployment theorem, class field theory correspondence, generalized class groups, idelic version, generalized norm residue symbol, number field satisfying, local reciprocity map, local norm residue symbol, abelian closure, norm conductor, ray class fields, restricted ramification, real infinite places, decomposition subfield, maximal abelian subextension, upper numbering, genus theory, global class field theory, ordinary class group, higher ramification groups, genus field, local class field theory, residue degree, lower numbering Key Phrases - Capitalized Phrases (CAPs): (learn more)
T-ramified S-split, Existence Theorems, Invariant Class Groups, S-split Hilbert, Compositum of the S-Split, T-principal S-units, Ahelian Extensions New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter gives the definitions of the objects which will be used throughout this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
global reciprocity map, deployment theorem, class field theory correspondence, generalized class groups, idelic version, generalized norm residue symbol, number field satisfying, local reciprocity map, local norm residue symbol, abelian closure, norm conductor, ray class fields, restricted ramification, real infinite places, decomposition subfield, maximal abelian subextension, upper numbering, genus theory, global class field theory, ordinary class group, higher ramification groups, genus field, local class field theory, residue degree, lower numbering Key Phrases - Capitalized Phrases (CAPs): (learn more)
T-ramified S-split, Existence Theorems, Invariant Class Groups, S-split Hilbert, Compositum of the S-Split, T-principal S-units, Ahelian Extensions New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 51
books:
See all 51 books this book cites
- Class Field Theory (Advanced Book Classics) by Emil Artin on 4 pages
- Number Theory by Wladyslaw Narkiewicz in Back Matter (1), Back Matter (2), and Back Matter (3)
- Number Theory by Helmut Hasse in Back Matter (1), Back Matter (2), and Back Matter (3)
- Algebraic Number Theory by H. Koch in Back Matter (1), and Back Matter (2)
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
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