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.
General
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