{
  "id": "0909.0969",
  "version": "v3",
  "published": "2009-09-04T21:50:02.000Z",
  "updated": "2010-07-01T16:38:55.000Z",
  "title": "Purity results for $p$-divisible groups and abelian schemes over regular bases of mixed characteristic",
  "authors": [
    "Adrian Vasiu",
    "Thomas Zink"
  ],
  "comment": "28 pages. Final version identical (modulo style) to the galley proofs. To appear in Doc. Math",
  "journal": "Doc. Math. 15 (2010), 571--599",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime. Let $(R,\\ideal{m})$ be a regular local ring of mixed characteristic $(0,p)$ and absolute index of ramification $e$. We provide general criteria of when each abelian scheme over $\\Spec R\\setminus\\{\\ideal{m}\\}$ extends to an abelian scheme over $\\Spec R$. We show that such extensions always exist if $e\\le p-1$, exist in most cases if $p\\le e\\le 2p-3$, and do not exist in general if $e\\ge 2p-2$. The case $e\\le p-1$ implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring $O$ of mixed characteristic $(0,p)$ and index of ramification at most $p-1$. This leads to large classes of examples of N\\'eron models over $O$. If $p>2$ and index $p-1$, the examples are new.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-07-01T16:38:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18",
      "14F30",
      "14G35",
      "14G40",
      "14K10",
      "14K15",
      "14L05",
      "14L15",
      "14J20"
    ],
    "keywords": [
      "abelian scheme",
      "mixed characteristic",
      "regular bases",
      "purity results",
      "divisible groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0969V"
    }
  }
}