Mathematische Zeitschrift

, Volume 244, Issue 4, pp 711–723

On Carlson's depth conjecture in group cohomology


DOI: 10.1007/s00209-003-0517-z

Cite this article as:
Green, D. Math. Z. (2003) 244: 711. doi:10.1007/s00209-003-0517-z


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Fachbereich 7 MathematikBergische Universität WuppertalWuppertalGermany