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