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1 June 2019 Purity for the Brauer group
Kęstutis Česnavičius
Duke Math. J. 168(8): 1461-1486 (1 June 2019). DOI: 10.1215/00127094-2018-0057

Abstract

A purity conjecture due to Grothendieck and Auslander–Goldman predicts that the Brauer group of a regular scheme does not change after removing a closed subscheme of codimension 2. The combination of several works of Gabber settles the conjecture except for some cases that concern p-torsion Brauer classes in mixed characteristic (0,p). We establish the remaining cases by using the tilting equivalence for perfectoid rings. To reduce to perfectoids, we control the change of the Brauer group of the punctured spectrum of a local ring when passing to a finite flat cover.

Citation

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Kęstutis Česnavičius. "Purity for the Brauer group." Duke Math. J. 168 (8) 1461 - 1486, 1 June 2019. https://doi.org/10.1215/00127094-2018-0057

Information

Received: 2 February 2018; Revised: 26 November 2018; Published: 1 June 2019
First available in Project Euclid: 18 May 2019

zbMATH: 07080116
MathSciNet: MR3959863
Digital Object Identifier: 10.1215/00127094-2018-0057

Subjects:
Primary: 14F22
Secondary: 14F20, 14G22, 16K50

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 8 • 1 June 2019
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