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Pinching Azumaya algebras
Published 13 Jul 2022 in math.AG | (2207.06344v2)
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.
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