Le Floc’h, Matthieu On Fitting ideals of certain étale \(K\)-groups. (English) Zbl 1083.11073 \(K\)-Theory 27, No. 3, 281-292 (2002). The author computes the first Fitting ideal of \(K^{\text{ét}}_{2i-2} (O^S_F) (\phi)\), showing it is principal and generated by a Brumer-Stickelberger element, where \(O^S_F\) is the \(S\)-integer ring of the abelian number field \(F/\mathbb{Q},\;\) \(S\) is a set of primes of \(F\) tamely or wildly ramified over the odd prim number \(p\), \(\phi\) is a character of Gal\((F/\mathbb{Q})\) of order prime to \(p\) different from the \(i\)th power of the Teichmüller character, and \(H(\phi)\) means \(e_\phi H\) with \(e_\phi\) the usual orthogonal idempotent. Reviewer: Zhang Xianke (Beijing) Cited in 2 Documents MSC: 11R70 \(K\)-theory of global fields 11R23 Iwasawa theory 19D50 Computations of higher \(K\)-theory of rings 19F27 Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) Keywords:K-theory étale K-group; Fitting ideal; Iwasawa module; Stickelberger element PDFBibTeX XMLCite \textit{M. Le Floc'h}, \(K\)-Theory 27, No. 3, 281--292 (2002; Zbl 1083.11073) Full Text: DOI