A Serre-Swan theorem for gerbe modules on \'etale Lie groupoids

Christoph Schweigert; Christopher Tropp; Alessandro Valentino

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arXiv · 1401.2824

A Serre-Swan theorem for gerbe modules on \'etale Lie groupoids

Christoph Schweigert·Christopher Tropp·Alessandro Valentino

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Abstract

Given a bundle gerbe on a compact smooth manifold or, more generally, on a compact \'etale Lie groupoid $M$, we show that the corresponding category of gerbe modules, if it is non-trivial, 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.

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BibTeX RIS

Christoph Schweigert, Christopher Tropp, Alessandro Valentino. 2014-01-13. A Serre-Swan theorem for gerbe modules on \'etale Lie groupoids. https://arxiv.org/abs/1401.2824

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