{
  "id": "math/0206127",
  "version": "v1",
  "published": "2002-06-12T14:22:51.000Z",
  "updated": "2002-06-12T14:22:51.000Z",
  "title": "On Carlson's depth conjecture in group cohomology",
  "authors": [
    "David J. Green"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-06-12T14:22:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06"
    ],
    "keywords": [
      "carlsons depth conjecture",
      "group cohomology",
      "cohomology ring",
      "duflots lower bound",
      "multiplication map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}