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A Serre-Swan theorem for gerbe modules on étale Lie groupoids. (English) Zbl 1315.53020

Summary: Given a torsion bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid \(M\), we show that the corresponding category of gerbe modules is equivalent to the category of finitely generated projective modules over an Azumaya algebra on \(M\). This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.

MSC:

53C08 Differential geometric aspects of gerbes and differential characters
55R65 Generalizations of fiber spaces and bundles in algebraic topology
22A22 Topological groupoids (including differentiable and Lie groupoids)
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