Ritter, J.; Weiss, A. On the local Galois structure of \(S\)-units. (English) Zbl 0819.11051 Frey, Gerhard (ed.) et al., Algebra and number theory. Proceedings of a conference held at the Institute of Experimental Mathematics, University of Essen, Germany, December 2-4, 1992. Berlin: de Gruyter. 229-245 (1994). Let \(K/h\) be a finite Galois extension of number fields and let \(S\) be a finite set of primes of \(K\), which is closed under the action of \(G\) and contains all the infinite primes. The paper is concerned with the problem of determining the \(\mathbb{Z} G\)-module structure of the group \(U\) of \(S\)- units of \(K\). The first main result is that under certain assumptions this structure is determined by the actions of \(G\) on \(\mu\) – the roots of unity in \(K\) – and on \(S\) and moreover by the coset of the third Chinburg invariant in a certain quotient group of \(\text{Cl} (\mathbb{Z} G)\). Moreover results are offered which relate this structure to certain Galois homomorphisms of Tate and of Fröhlich.For the entire collection see [Zbl 0793.00015]. Reviewer: J.Brinkhuis (Rotterdam) Cited in 1 ReviewCited in 2 Documents MSC: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers Keywords:local Galois structure; Galois module; Stark’s conjecture; \(S\)-units; third Chinburg invariant; Galois homomorphisms PDFBibTeX XMLCite \textit{J. Ritter} and \textit{A. Weiss}, in: Algebra and number theory. Proceedings of a conference held at the Institute of Experimental Mathematics, University of Essen, Germany, December 2-4, 1992. Berlin: de Gruyter. 229--245 (1994; Zbl 0819.11051)