The formula of 8-ranks of tame kernels
type: Item
instance of: scholarly article
title: The formula of 8-ranks of tame kernels
zbMATH Open document ID: 1063.11039
author: Qin Yue
published in: Journal of Algebra
publication date: 2005-04-21T00:00:00Z
review text: Let \(d\) be a squarefree integer that can be written in the form \(d = u^2 - 2w^2\), and consider the quadratic number fields \(F = \mathbb Q(\sqrt{d}\,)\) and \(E = \mathbb Q(\sqrt{-d}\,)\). The author proves that the \(8\)-rank of \(K_2({\mathcal O}_F)\) and the \(8\)-rank of the class group of \(E\) in the strict sense differ at most by \(1\). The main tools are the results of \textit{H.~Qin} [J. Reine Angew. Math. 530, 105--144 (2001; Zbl 1003.11052)] as well as Rédei matrices and results on the solvability of ternary quadratic forms \(aX^2 + bY^2 + cZ^2 = 0\).
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 19C20
zbMATH DE Number: 2159733
zbMATH Keywords: tame kernel
zbMATH Keywords: class group
zbMATH Keywords: genus theory
zbMATH Keywords: redei matrices
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.10.030
OpenAlex ID: W2078374122
cites work: On Sylow 2-subgroups of K2OF for quadratic number fields F.
cites work: On the 4-rank of the tame kernel \(K_2(\mathcal O)\) in positive definite terms
cites work: Q4739993
cites work: Tame kernels under relative quadratic extensions and Hilbert symbols
cites work: The structure of the 2-Sylow-subgroup of \(K_ 2({\mathfrak o})\). I
cites work: The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields
cites work: Q4526959
cites work: Relations between \(K_2\) and Galois cohomology
cites work: Elements of order 4 of the Hilbert kernel in quadratic number fields
cites work: Dyadic ideal, class group, and tame kernel in quadratic fields
cites work: On tame kernel and class group in terms of quadratic forms.
cites work: The 4-rank of the tame kernel versus the 4-rank of the narrow class group in quadratic number fields
DOI: 10.1016/J.JALGEBRA.2004.10.030
description: scientific article; zbMATH DE number 2159733