On the separation of connected components by étale cohomology
type: Item
instance of: scholarly article
title: On the separation of connected components by étale cohomology
zbMATH Open document ID: 0866.19003
DOI: 10.1007/BF00998128
author: Louis Mahé
published in: \(K\)-Theory
publication date: 1997-07-17T00:00:00Z
review text: In this paper a new proof that for any connected component \(C\) of the real spectrum of a ring, it is possible to find a cohomology class whose signature separates \(C\) from its complement is given (former proofs had been given by Colliot-Thélène and Parimala, Buresi and Scheiderer). The new proof follows the pattern of the proof formerly given by Mahé for the separation of connected components by quadratic forms, making thus the analogy between the two situations more clear.
Mathematics Subject Classification ID: 19F27
Mathematics Subject Classification ID: 14P05
zbMATH DE Number: 827891
zbMATH Keywords: connected component of real spectrum of ring
zbMATH Keywords: cohomology class
zbMATH Keywords: signature
reviewed by: Marie-Françoise Roy
MaRDI profile type: Publication
cites work: Local-global principle for étale cohomology
cites work: Real components of algebraic varieties and étale cohomology
cites work: Localisation de formes quadratiques $I$
cites work: Signatures et composantes connexes
cites work: Pfister's theorem for varieties and reduced Witt rings
cites work: Q4101953
cites work: Real and étale cohomology
full work available at URL: https://doi.org/10.1007/bf00998128
OpenAlex ID: W2014721399
description: scientific article; zbMATH DE number 827891