  We introduce the notion of being cohomologically complete for objects of the
derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then
we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove
coherency results by using the property of being cohomologically complete.
  We apply these results to the study of modules over deformation quantization
algebroids on complex Poisson manifolds. We prove in particular that under a
natural properness condition, the convolution of two coherent kernels over such
algebroids is coherent. We also construct the dualizing complexes in this
framework and show that the convolution of kernels commutes with duality.
