On the Brauer group of a Laurent polynomial ring
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.
scientific article; zbMATH DE number 4059546
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