Galois Module Structure of Algebraic Integers: 1 (Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics) - Hardcover

Frohlich, A.

Hardcover

ISBN 10: 3540119205 ISBN 13: 9783540119203

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1983

Synopsis

In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.

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Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1983
• Language: English
• ISBN 10: 3540119205
• ISBN 13: 9783540119203
• Binding: Hardcover
• Number of pages: 276