A Serre-Swan theorem for gerbe modules on étale Lie groupoids

2014/01/13 by Schweigert, Christoph, Tropp, Christopher, Valentino, Alessandro · 1 citation
#Algebraic Topology (math.AT) #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.2824

Abstract

Given a 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, 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.

Cited by

• Classification of derived Azumaya Algebras over derived smooth manifolds via derived Brauer Groups

Related

• Lie groupoids and crossed module-valued gerbes over stacks
• A Serre-Swan theorem for bundles of bounded geometry
• Gerbes and Lie Groups
• A singular Serre-Swan theorem via tepui fibrations
• A classification of equivariant gerbe connections