Extending Derived Azumaya Algebras to Derived Smooth Manifolds
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More information: Conference on “New Perspectives on Stable Homotopy and Beyond”
We transport Toën’s categorical derived Brauer stack to the setting of derived smooth manifolds in the sense of Spivak. Using the forgetful functor from simplicial $C^\infty$-rings to simplicial commutative rings, we evaluate Toën’s construction locally and then stackify it on the open site of a derived smooth manifold. This yields a smooth categorical Brauer stack and a corresponding classification of derived Brauer classes, extending part of Toën’s framework to derived differential geometry. A preliminary version is available at arXiv:2607.22668
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