Mukai duality for gerbes with connection

Details Mukai duality for gerbes with connection Mukai duality for gerbes with connection

2008-03-11

arxiv.org/abs/0803.1529v2

Mathematics

Quantum Algebra

Final version. To appear in Crelle's journal

Scientific paper

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.

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