  We explain how Cohen--Macaulay classifying spaces are ubiquitous among
discrete groups that satisfy Bieri--Eckmann duality, and compare Bieri--Eckmann
duality to duality results for Cohen--Macaulay complexes. We use this
comparison to give a description of the dualizing module of ${\rm{Out}}(F_N)$
in terms of the local cohomology cosheaf of the spine of Outer space.
