On Carlson's depth conjecture in group cohomology
David Green

We establish a weak form of Carlson's conjecture on the depth
of the mod-p cohomology ring of a p-group. In particular, 
Duflot's lower bound for the depth is tight if and only if
the cohomology ring is not detected on a certain family of
subgroups. The proofs use the structure of the cohomology ring
as a comodule over the cohomology of the centre via the
multiplication map. We demostrate the existence of a set of
parameters (so-called polarised systems) which are particularly
well adapted to this comodule structure.