Sheaf theory for stacks in manifolds and twisted cohomology for S^1-gerbes

摘要

This is the first of a series of papers on sheaf theory on smooth andtopological stacks and its applications. The main result of the present paperis the characterization of the twisted (by a closed integral three-form) deRham complex on a manifold. As an object in the derived category it will berelated with the push-forward of the constant sheaf from a S^1-gerbe withDixmier-Douady class represented by the three-form. In order to formulate andprove this result we develop in detail the foundations of sheaf theory forsmooth stacks.