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arXiv · 2207.06344

Pinching Azumaya algebras

Johannes Fischer
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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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Johannes Fischer. 2022-07-13. Pinching Azumaya algebras. https://doi.org/10.1016/j.jpaa.2023.107406

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