%0 Journal Article
%T Mukai duality for gerbes with connection
%A Jonathan Block
%A Calder Daenzer
%J Mathematics
%D 2008
%I arXiv
%X We study gerbes with connection over an etale stack via noncommutative algebras of differential forms on a groupoid presenting the stack. We then describe a dg-category of modules over any such algebra, which we claim represents a dg-enhancement of the derived category of coherent analytic sheaves on the gerbe in question. This category can be used to phrase and prove Fourier-Mukai type dualities between gerbes and other noncommutative spaces. As an application of the theory, we show that a gerbe with flat connection on a torus is dual (in a sense analogous to Fourier-Mukai duality or T-duality) to a noncommutative holomorphic dual torus.
%U http://arxiv.org/abs/0803.1529v2