Pinching Azumaya algebras
arXiv:2207.06344 · doi:10.1016/j.jpaa.2023.107406
Abstract
We show, that for a morphism of schemes from X to Y, that is a finite modification in finitely many closed points, a cohomological Brauer class on Y is represented by an Azumaya algebra if its pullback to X is represented by an Azumaya algebra. Part of the proof uses an extension of a result by Ferrand, on pinching of finite locally free sheaves, to Azumaya algebras.
minor changes, to appear in J. Pure Appl. Algebra