English

On Carlson's depth conjecture in group cohomology

Algebraic Topology 2015-02-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0206127,
  title  = {On Carlson's depth conjecture in group cohomology},
  author = {David J. Green},
  journal= {arXiv preprint arXiv:math/0206127},
  year   = {2015}
}

Comments

10 pages