Purity for the Brauer group

Mardi 16 janvier 14:15-15:15 - Kestutis Cesnavicius - Orsay

Résumé : 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.

Lieu : IMO Bât. 307, salle 3L15

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