Multiplicative Galois module structure
type: Item
instance of: scholarly article
title: Multiplicative Galois module structure
zbMATH Open document ID: 0856.11050
author: A. Weiss
published in: Fields Institute Monographs
publication date: 1996-07-04T00:00:00Z
review text: This booklet is the result of a short course on the Galois module structure of the \(S\)-units of a number field, which was given in 1993 at the Fields Institute (Canada). The main theme is that this structure should be determined by cohomological class field theory and by the behaviour at \(s=0\) of Artin \(L\)-functions. The course covers such classical topics as Fröhlich's idelic Hom-description, Tate's exact sequence and \(q\)-index (for \(S\) large), Chinburg invariants, conjectures of Stark and allied \dots The new angle is to use homotopy of modules and the formalism of Weil groups, as in \textit{K. W. Gruenberg} and the author [Proc. Lond. Math. Soc., III. Ser. 70, No. 2, 264-284 (1995; Zbl 0828.11062), and \textit{J. Ritter} and the author, Compos. Math. 102, No. 2, 147-178 (1996)], to give a unified treatment and deal with the case of small \(S\).
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 11R42
zbMATH DE Number: 896974
zbMATH Keywords: Galois module structure
zbMATH Keywords: \(S\)-units
zbMATH Keywords: number field
zbMATH Keywords: cohomological class field theory
zbMATH Keywords: Artin \(L\)-functions
zbMATH Keywords: Hom-description
zbMATH Keywords: Tate's exact sequence
zbMATH Keywords: \(q\)-index
zbMATH Keywords: Chinburg invariants
zbMATH Keywords: homotopy of modules
zbMATH Keywords: Weil groups
reviewed by: Thong Nguyen Quang Do
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 896974