{
  "id": "1306.3385",
  "version": "v3",
  "published": "2013-06-14T12:53:23.000Z",
  "updated": "2013-10-15T15:51:19.000Z",
  "title": "Extensions for Finite Chevalley Groups III: Rational and Generic Cohomology",
  "authors": [
    "Christopher P. Bendel",
    "Daniel K. Nakano",
    "Cornelius Pillen"
  ],
  "comment": "Corrected proof of Theorem 5.1.1, added Remark 5.2.3",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected reductive algebraic group and $B$ be a Borel subgroup defined over an algebraically closed field of characteristic $p>0$. In this paper, the authors study the existence of generic $G$-cohomology and its stability with rational $G$-cohomology groups via the use of methods from the authors' earlier work. New results on the vanishing of $G$ and $B$-cohomology groups are presented. Furthermore, vanishing ranges for the associated finite group cohomology of $G({\\mathbb F}_{q})$ are established which generalizes earlier work of Hiller, in addition to stability ranges for generic cohomology which improves on seminal work of Cline, Parshall, Scott and van der Kallen.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-15T15:51:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G10"
    ],
    "keywords": [
      "finite chevalley groups",
      "generic cohomology",
      "cohomology groups",
      "extensions",
      "associated finite group cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3385B"
    }
  }
}