On a Hasse principle for \(\sigma\)-conjugacy
type: Item
instance of: scholarly article
title: On a Hasse principle for \(\sigma\)-conjugacy
zbMATH Open document ID: 0704.11052
author: Hiroshi Saito
published in: Journal of Mathematics of Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: Let G be an algebraic group defined over the number field K such that \(G(K)=A^{\times}\), where A is a semisimple algebra over K. If M is a cyclic extension of K with generator \(\sigma\) of the Galois group one studies the \(\sigma\)-conjugacy classes in G(M) (i.e., g and \(g'\) belong to the same class if \(g'=h^{-1}g^{\sigma}h\) for some h). It is shown that \(\sigma\)-conjugacy classes are mapped bijectively by a natural norm map to the \(\sigma\)-invariant conjugacy classes which are locally everywhere in the image of that map. As a consequence one sees that two elements of G(M) are \(\sigma\)-conjugate if and only if they are \(\sigma\)-conjugate locally everywhere.
Mathematics Subject Classification ID: 11R54
zbMATH DE Number: 4154566
zbMATH Keywords: Hasse principle
zbMATH Keywords: twisted conjugacy classes
zbMATH Keywords: semisimple algebra
zbMATH Keywords: Galois group
reviewed by: Rainer Schulze-Pillot
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520176
OpenAlex ID: W1560437066
DOI: 10.1215/KJM/1250520176
description: scientific article; zbMATH DE number 4154566