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 at least 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.