  The paper describes a duality phenomenon for cohomology theories with the
character of Gorenstein rings. For a connective cohomology theory with the
p-local integers in degree 0, and coefficient ring R_* Gorenstein of shift 0,
this states that for X with R_*(X) torsion, we have R^*(X)=\Sigma^a Hom(
R_*(X), Z/p^{\infty}). A corresponding statement for modules over a commutative
Gorenstein ring spectrum is also proved. [Minor typographical and bibliographic
changes to the last version.]
