\(K\)-groups and \(\lambda\)-invariants of algebraic number fields
type: Item
instance of: scholarly article
title: \(K\)-groups and \(\lambda\)-invariants of algebraic number fields
zbMATH Open document ID: 0699.12020
author: Keiichi Komatsu
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let \(F\) be a totally real number field and \(p\neq 2\) a prime. Let \(F'\) be a Galois \(p\)-extension of \(F\). Then the author gives sufficient conditions for the \(p\)-divisibility of \(| K_{2n}(O_{F'})|\) for \(n\) odd (essentially ramification conditions in the extension \(F'_{\infty}/F_{\infty}\) built with cyclotomic \(\mathbb Z_ p\)-extensions of \(F\), \(F'\)). The author uses Iwasawa's theory via a result of Galois descent of \textit{C. Soulé} [Invent. Math. 55, 251--295 (1979; Zbl 0437.12008)] and supposes that the \(\mu\)-invariant of \(F(\exp(2i\pi/p))\) is zero. Remark. The point (4) of the main theorem \((n=1)\) is now known in full generality by means of the concept of primitive ramification and regular fields [see the bibliography in \textit{G. Gras} and \textit{J.-F. Jaulent}, Math. Z. 202, No. 3, 343--365 (1989; Zbl 0704.11040)].
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 4146061
zbMATH Keywords: Tame kernel
zbMATH Keywords: Hilbert kernel
zbMATH Keywords: Quillen's higher K-group
zbMATH Keywords: p-divisibility
zbMATH Keywords: Iwasawa's theory
reviewed by: Georges Gras
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133970
OpenAlex ID: W2076176202
DOI: 10.3836/TJM/1270133970
description: scientific article; zbMATH DE number 4146061