Higher degree tame Hilbert-symbol equivalence of number fields
type: Item
instance of: scholarly article
title: Higher degree tame Hilbert-symbol equivalence of number fields
zbMATH Open document ID: 0968.11038
DOI: 10.1007/BF02940871
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2000-03-19T00:00:00Z
review text: The main aim of the paper is to give necessary and sufficient conditions for the tame degree \(\ell\) Hilbert-symbol equivalence of two number fields \(K\) and \(L\) where \(\ell\) is an odd prime. The conditions are expressed in terms of the classical invariants, and are similar to those given in the author's paper [Acta Arith. 58, 29-46 (1991; Zbl 0733.11012)] for the case where \(\ell=2\) and \(K\), \(L\) are quadratic number fields. Moreover, the author finds some new invariants of the tame degree \(\ell\) Hilbert-symbol equivalence, among them the \(\ell\)-rank of the tame kernel \({\mathbb K}_2({\mathcal O}_K)\), thus generalizing one of the results proved by \textit{P. E. Conner, R. Perlis} and \textit{K. Szymiczek} [Acta Arith. 79, 83-91 (1997; Zbl 0880.11039)].
reviewed by: Roberto Dvornicich
Mathematics Subject Classification ID: 11R21
Mathematics Subject Classification ID: 19F15
Mathematics Subject Classification ID: 11E81
zbMATH DE Number: 1416697
zbMATH Keywords: Hilbert-symbol equivalence
zbMATH Keywords: tame kernels
author: Alfred Czogała
Wikidata QID: Q29397984
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1416697