{
  "id": "1109.2093",
  "version": "v5",
  "published": "2011-09-09T18:58:50.000Z",
  "updated": "2012-01-17T20:28:59.000Z",
  "title": "On the Hasse principle for finite group schemes over global function fields",
  "authors": [
    "Cristian D. Gonzalez-Aviles",
    "Ki-Seng Tan"
  ],
  "comment": "A \"Concluding Remarks\" Section added",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let K be a global function field of positive characteristic p and let M be a (commutative) finite and flat K-group scheme. We show that the kernel of the canonical localization map H^{1}(K,M)\\to\\prod_{all v}H^{1}(K_{v},M) in flat (fppf) cohomology can be computed solely in terms of Galois cohomology. We then give applications to the case where M is the kernel of multiplication by p^{m} on an abelian variety defined over K.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-01-17T20:28:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14K15"
    ],
    "keywords": [
      "global function field",
      "finite group schemes",
      "hasse principle",
      "flat k-group scheme",
      "abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2093G"
    }
  }
}