A Serre-Swan theorem for gerbe modules on \'etale Lie groupoids
Algebraic Topology
2014-01-14 v1 Category Theory
Differential Geometry
Abstract
Given a bundle gerbe on a compact smooth manifold or, more generally, on a compact \'etale Lie groupoid , 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 . This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.
Cite
@article{arxiv.1401.2824,
title = {A Serre-Swan theorem for gerbe modules on \'etale Lie groupoids},
author = {Christoph Schweigert and Christopher Tropp and Alessandro Valentino},
journal= {arXiv preprint arXiv:1401.2824},
year = {2014}
}
Comments
13 pages