{
  "id": "0811.3852",
  "version": "v1",
  "published": "2008-11-24T13:23:53.000Z",
  "updated": "2008-11-24T13:23:53.000Z",
  "title": "Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups",
  "authors": [
    "Roland Lötscher"
  ],
  "comment": "34 pages, no figures",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced by H.Kraft, G.Schwarz and the author. We generalize the central extension theorem of Buhler and Reichstein and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev about the essential dimension of p-groups. One part of this paper is devoted to the study of completely reducible faithful representations. Amongst results concerning faithful representations of minimal dimension there is a computation of the minimal number of irreducible components needed for a faithful representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-24T13:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "14L30",
      "20C20"
    ],
    "keywords": [
      "essential dimension",
      "finite groups",
      "multihomogeneous covariants",
      "application",
      "central extension theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.3852L"
    }
  }
}