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arXiv · 1711.06456

Purity for the Brauer group

Kestutis Cesnavicius
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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 $\ge 2$. 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.

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Kestutis Cesnavicius. 2017-11-17. Purity for the Brauer group. https://doi.org/10.1215/00127094-2018-0057

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