{
  "id": "0911.2474",
  "version": "v3",
  "published": "2009-11-12T21:03:21.000Z",
  "updated": "2012-04-16T15:07:36.000Z",
  "title": "Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic",
  "authors": [
    "Adrian Vasiu",
    "Thomas Zink"
  ],
  "comment": "25 pages. Final version to appear in J. Number Theory",
  "journal": "J. Number Theory 132 (2012), no. 9, 2003-2019",
  "doi": "10.1016/j.jnt.2012.03.010",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $p$ be a prime. Let $V$ be a discrete valuation ring of mixed characteristic $(0,p)$ and index of ramification $e$. Let $f: G \\rightarrow H$ be a homomorphism of finite flat commutative group schemes of $p$ power order over $V$ whose generic fiber is an isomorphism. We provide a new proof of a result of Bondarko and Liu that bounds the kernel and the cokernel of the special fiber of $f$ in terms of $e$. For $e < p-1$ this reproves a result of Raynaud. Our bounds are sharper that the ones of Liu, are almost as sharp as the ones of Bondarko, and involve a very simple and short method. As an application we obtain a new proof of an extension theorem for homomorphisms of truncated Barsotti--Tate groups which strengthens Tate's extension theorem for homomorphisms of $p$-divisible groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-04-16T15:07:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18",
      "11S25",
      "11S31",
      "14F30",
      "14G35",
      "14K10",
      "14L05"
    ],
    "keywords": [
      "finite flat group schemes",
      "discrete valuation ring",
      "mixed characteristic",
      "boundedness results",
      "strengthens tates extension theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.2474V"
    }
  }
}