Abstract Kęstutis Česnavičius

Purity for the Brauer group

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 will discuss an approach to the mixed characteristic case via the tilting equivalence for perfectoid rings.