D.J. Benson and J.P.C. Greenlees
Commutative algebra for cohomology rings of virtual duality groups.
Preprint, 1996.
\begin{abstract}
Cohomology rings  of finite groups have strong duality properties, 
as shown by  Benson and Carlson \cite{bc5}, and Greenlees \cite{groupca}. 
We prove here that   cohomology rings  of   virtual duality groups
have  a ring theoretic duality property, which combines
the duality properties of finite groups
with the cohomological duality of the subgroup of finite index.
The formal behaviour of the local cohomology theorem 
is  precisely analogous to that for a compact Lie group~\cite{bg2},
except that the dimension appears to be negative.
\end{abstract}