Authors: J.P.C.Greenlees and G.Lyubeznik 
``Rings with a local cohomology theorem, and  applications to group 
cohomology.'' 17 pp

We study connected graded algebra over a field which satisfy a local 
cohomology theorem (such as the cohomology ring of a group which is 
a discrete or profinite virtual duality group or a compact Lie group). 
It is obvious that if such a ring is Cohen-Macaulay it is Gorenstein.
We show that if it  has depth one less than  its dimension (ie is almost
Cohen-Macaulay) then it is in fact almost Gorenstein, and its Hilbert series
satisfies a pair of functional equations. This proves a conjecture of 
Greenlees and Benson for the cohomology of classifying spaces of compact
Lie groups and virtual duality groups. We also prove a number of structural 
results. For example, minimal primes of local cohomology 
groups of cohomology rings of groups are shown to be Quillen strata.  

Status: Submitted for publication.