Self-equivalences of the Gaussian field
type: Item
instance of: scholarly article
title: Self-equivalences of the Gaussian field
zbMATH Open document ID: 1239.11047
DOI: 10.1216/RMJ-2008-38-6-2077
author: Marius Somodi
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-04-07T00:00:00Z
review text: Self-equivalence of a number field \(K\) is a Hilbert-symbol equivalence of \(K\) with itself (for explanation what a Hilbert-symbol equivalence is, see the reviews of the earlier work of the author: [Can. J. Math. 57, No. 1, 180--203 (2005; Zbl 1073.11026)] or [Acta Arith. 121, No. 4, 327--334 (2006; Zbl 1115.11024)]. The wild set of a self-equivalence of \(K\) is the set of wild primes, that is, of finite primes \(P\) of \(K\) with the property that the parity of the \(P\)-order of elements of \(K\) is not preserved under the equivalence. Here the author proves that any finite set of primes of the Gaussian field \(\mathbb Q{(\sqrt{-1}\,)}\) occurs as the wild set of a self-equivalence of the field.
reviewed by: Kazimierz Szymiczek
Mathematics Subject Classification ID: 11E81
zbMATH DE Number: 5541311
zbMATH Keywords: Hilbert symbol equivalence
zbMATH Keywords: Gaussian self-equivalence
zbMATH Keywords: tame
zbMATH Keywords: wild
MaRDI profile type: Publication
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full work available at URL: rmj-2008-38-6-2077
OpenAlex ID: W2048863560
description: scientific article; zbMATH DE number 5541311