Geodesic
A Serre-Swan theorem for gerbe modules on étale Lie groupoids
Theory and applications of categories, Tome 29 (2014), pp. 819-835

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 53C08, 55R65, 22A22
Keywords: Gerbe modules, Lie groupoids, Serre-Swann theorem 
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     author = {Christoph Schweigert and Christopher Tropp and Alessandro Valentino},
     title = {A {Serre-Swan} theorem for gerbe modules on \'etale {Lie} groupoids},
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Christoph Schweigert; Christopher Tropp; Alessandro Valentino. A Serre-Swan theorem for gerbe modules on étale Lie groupoids. Theory and applications of categories, Tome 29 (2014), pp. 819-835. http://geodesic.mathdoc.fr/item/TAC_2014_29_a27/