On the Brauer group of a Laurent polynomial ring
type: Item
instance of: scholarly article
title: On the Brauer group of a Laurent polynomial ring
zbMATH Open document ID: 0649.13002
DOI: 10.1016/0022-4049(88)90081-3
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: For R a commutative Noetherian ring, t an indeterminate, the author describes the n-torsion part of the Brauer group of R[t,1/t] for any n relatively prime to all of the residue characteristics of R. This extends a result of \textit{R. T. Hoobler} [in Methods in ring theory, Proc. NATO Adv. Study Inst., Antwerp/Belg. 1983, NATO ASI Ser., Ser. C 129, 161-170 (1984; Zbl 0555.16002)] for R a Noetherian normal domain, which in turn extends results of \textit{A. R. Magid} [Proc. Am. Math. Soc. 71, 164-168 (1978; Zbl 0393.20029)] and \textit{F. R. DeMeyer} [Brauer Groups, Proc. Conf. Evanston 1975, Lect. Notes Math. 549, 16-24 (1976; Zbl 0337.13006)]. The result is obtained via an extended application of étale cohomology theory. Two examples involving affine rings of singular cubic plane curves conclude the paper.
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 4059546
zbMATH Keywords: Laurent polynomial ring
zbMATH Keywords: Rees ring
zbMATH Keywords: torsion part of the Brauer group
zbMATH Keywords: étale cohomology
zbMATH Keywords: singular cubic plane curves
author: Timothy J. Ford
reviewed by: Lindsay N. Childs
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90081-3
OpenAlex ID: W2013092098
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description: scientific article; zbMATH DE number 4059546