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On the Galois module structure over CM-fields

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Abstract

In this paper we make a contribution to the problem of the existence of a normal integral basis. Our main result is that unramified realizations of a given finite abelian group Δ as a Galois group Gal (N/K) of an extensionN of a givenCM-fieldK are invariant under the involution on the set of all realizations of Δ overK which is induced by complex conjugation onK and by inversion on Δ. We give various implications of this result. For example, we show that the tame realizations of a finite abelian group Δ of odd order over a totally real number fieldK are completely characterized by ramification and Galois module structure.

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  1. Econometric Institute, Erasmus University, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    Jan Brinkhuis

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  1. Jan Brinkhuis
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Brinkhuis, J. On the Galois module structure over CM-fields. Manuscripta Math 75, 333–347 (1992). https://doi.org/10.1007/BF02567089

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  • DOI: https://doi.org/10.1007/BF02567089

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