{
  "id": "1112.4603",
  "version": "v1",
  "published": "2011-12-20T08:34:31.000Z",
  "updated": "2011-12-20T08:34:31.000Z",
  "title": "Stratified bundles and étale fundamental group (new version)",
  "authors": [
    "Hélène Esnault",
    "Xiaotao Sun"
  ],
  "comment": "This submission replaces the arXiv:1012.5381 submission with the same title, which had been withdrawn as it contained a mistake, repaired in this submission. 18 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "This submission replaces the arXiv:1012.5381 submission with the same title, which had been withdrawn as it contained a mistake, repaired in this submission: on $X$ projective smooth over an algebraically closed field of characteristic $p>0$, we show that all irreducible stratified bundles have rank 1 if and only if the commutator $[\\pi_1, \\pi_1]$ of the \\'etale fundamental group $\\pi_1$ is a pro-$p$-group, and we show that the category of stratified bundles is semi-simple with irreducible objects of rank 1 if and only if $ \\pi_1 $ is abelian without $p$-power quotient. This answers positively a conjecture by Gieseker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-20T08:34:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "etale fundamental group",
      "submission replaces",
      "power quotient",
      "projective smooth",
      "algebraically closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4603E"
    }
  }
}