  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 demonstrate
the existence of systems of parameters (so-called polarised systems) which are
particularly well adapted to this comodule structure.
