On tame kernel and class group in terms of quadratic forms.
type: Item
instance of: scholarly article
title: On tame kernel and class group in terms of quadratic forms.
zbMATH Open document ID: 1035.11058
author: Qin Yue
published in: Journal of Number Theory
publication date: 2003-03-23T00:00:00Z
review text: In [J. Number Theory 88, 263--282 (2001; Zbl 0985.11059)], \textit{P. E. Conner} and \textit{J. Hurrelbrink} characterized the possible \(4\)-ranks of the tame kernels \(K_2(O_F)\) of quadratic number fields \(F\), whose discriminants have exactly two odd prime divisors \(p \equiv -1 \bmod 8\), \(l \equiv 1 \bmod 8\), satisfying \((\frac{p}{l}) = 1\), in terms of positive definite quadratic forms. In the paper under consideration the author treats the other two interesting cases of two odd discriminant divisors: \(p \equiv l \equiv 1 \bmod 8\) and \(p \equiv l \equiv -1 \bmod 8\), and at the same time extends the results to include information about the \(8\)-rank of the tame kernel, and the relations to the structure of the \(2\)-part of the class groups.
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 1886725
zbMATH Keywords: quadratic fields
zbMATH Keywords: genus theory
zbMATH Keywords: unramified cyclic degree 4 extension
reviewed by: Manfred Kolster
MaRDI profile type: Publication
full work available at URL: jnth.2002.2808
OpenAlex ID: W2082820938
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DOI: 10.1006/JNTH.2002.2808
description: scientific article; zbMATH DE number 1886725