{
  "id": "0808.2792",
  "version": "v3",
  "published": "2008-08-20T17:18:46.000Z",
  "updated": "2009-09-03T19:49:51.000Z",
  "title": "Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension",
  "authors": [
    "Adrian Vasiu",
    "Thomas Zink"
  ],
  "comment": "20 pages. Final version to appear in Advanced Studies in Pure Mathematics, Proceeding of Algebraic and Arithmetic Structures of Moduli Spaces, Hokkaido University, Sapporo, Japan, September 2007",
  "journal": "Advanced Studies in Pure Mathematics 58 (2010), 461-479",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $k$ be a perfect field of characteristic $p \\geq 3$. We classify $p$-divisible groups over regular local rings of the form $W(k)[[t_1,...,t_r,u]]/(u^e+pb_{e-1}u^{e-1}+...+pb_1u+pb_0)$, where $b_0,...,b_{e-1}\\in W(k)[[t_1,...,t_r]]$ and $b_0$ is an invertible element. This classification was in the case $r = 0$ conjectured by Breuil and proved by Kisin.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-09-03T19:49:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18",
      "14F30",
      "14G35",
      "14K10",
      "14L05"
    ],
    "keywords": [
      "regular local rings",
      "divisible groups",
      "arbitrary dimension",
      "breuils classification",
      "perfect field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.2792V"
    }
  }
}