Cohomology of Ample Groupoids via Flat Resolutions
A cochain-complex definition of the cohomology of an ample (etale, locally compact totally disconnected) groupoid: build a flat resolution defining the groupoid's homology with integer coefficients, then take cohomology with values in a groupoid module. The construction is proved to coincide with the earlier continuous-cocycle cohomology, hence is invariant under Morita equivalence; it yields an exact sequence for skew products by an integer-valued cocycle and explicit computations for AF-groupoids and certain action groupoids.
Cohomology of ample groupoids
We introduce a cochain complex for ample groupoids $\mathcal G$ using a flat resolution defining their homology with coefficients in $\mathbb Z$. We prove that the cohomology of this cochain complex …