{
  "id": "1204.0729",
  "version": "v2",
  "published": "2012-04-03T16:33:49.000Z",
  "updated": "2013-07-20T14:28:13.000Z",
  "title": "On projective modules for Frobenius kernels and finite Chevalley groups",
  "authors": [
    "Christopher M. Drupieski"
  ],
  "comment": "7 pages. This version corrects a minor error in the paragraph before, and in the proof of, Theorem 3.3. The error appears in the published version",
  "journal": "Bull. London Math. Soc. (2013) 45 (4): 715-720",
  "doi": "10.1112/blms/bds105",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "Let $G$ be a simply-connected semisimple algebraic group scheme over an algebraically closed field of characteristic $p > 0$. Let $r \\geq 1$ and set $q = p^r$. We show that if a rational $G$-module $M$ is projective over the $r$-th Frobenius kernel $G_r$ of $G$, then it is also projective when considered as a module for the finite subgroup $\\Gfq$ of $\\Fq$-rational points in $G$. This salvages a theorem of Lin and Nakano (\\emph{Bull.\\ London Math.\\ Soc.} 39 (2007) 1019--1028). We also show that the corresponding statement need not hold when the group $G$ is replaced by the unipotent radical $U$ of a Borel subgroup of $G$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-20T14:28:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G10",
      "20C33",
      "20G05",
      "17B56"
    ],
    "keywords": [
      "finite chevalley groups",
      "projective modules",
      "simply-connected semisimple algebraic group scheme",
      "th frobenius kernel",
      "finite subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0729D"
    }
  }
}