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Galois Module Structure of Algebraic Integers

  • Book
  • © 1983

Overview

Authors:
  1. Albrecht Fröhlich

    1. Imperial College London and Robinson College Cambridge, UK

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Albrecht Fröhlich
    Pages 1-2

  3. Notation and Conventions

    • Albrecht Fröhlich
    Pages 3-6

  4. Survey of Results

    • Albrecht Fröhlich
    Pages 7-52

  5. Classgroups and Determinants

    • Albrecht Fröhlich
    Pages 53-101

  6. Resolvents, Galois Gauss Sums, Root Numbers, Conductors

    • Albrecht Fröhlich
    Pages 102-147

  7. Congruences and Logarithmic Values

    • Albrecht Fröhlich
    Pages 148-198

  8. Root Number Values

    • Albrecht Fröhlich
    Pages 199-218

  9. Relative Structure

    • Albrecht Fröhlich
    Pages 219-248

  10. Back Matter

    Pages 249-262
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Keywords

About this book

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.

Authors and Affiliations

  • Imperial College London and Robinson College Cambridge, UK

    Albrecht Fröhlich

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