The Picard Homotopy Type of a Derived Smooth Manifold
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More information: Interactions between operator algebras, K-theory and homotopy theory
We construct an Picard–Brauer object for derived smooth manifolds in the sense of Spivak. After spectralizing the smooth structure sheaf, we prove open hyperdescent for the associated module categories and compute the resulting hypersheaf of invertible modules. For ordinary smooth manifolds, the construction recovers the expected real and complex cohomological invariants.
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