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.
Rezensionen / Stimmen
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)
