Multiplicative Galois module structure (Q1917143)

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 \(S\).