{
  "id": "math/0607508",
  "version": "v2",
  "published": "2006-07-20T16:13:42.000Z",
  "updated": "2010-06-15T15:51:57.000Z",
  "title": "Deformation subspaces of p-divisible groups as formal Lie groups associated to p-divisible groups",
  "authors": [
    "Adrian Vasiu"
  ],
  "comment": "36 pages. To appear in J. Alg. Geom",
  "journal": "J. Alg. Geom., Vol. 20 (2011), no. 1, 1-45",
  "doi": "10.1090/S1056-3911-2010-00571-1",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $k$ be an algebraically closed field of characteristic $p>0$. Let $D$ be a $p$-divisible group over $k$ which is not isoclinic. Let $\\scrD$ (resp. $\\scrD_k$) be the formal deformation space of $D$ over $\\Spf(W(k))$ (resp. over $\\Spf(k)$). We use axioms to construct formal subschemes $\\scrG_k$ of $\\scrD_k$ that: (i) have canonical structures of formal Lie groups over $\\Spf(k)$ associated to $p$-divisible groups over $k$, and (ii) give birth, via all geometric points $\\Spf(K)\\to\\scrG_k$, to $p$-divisible groups over $K$ that are isomorphic to $D_K$. We also identify when there exist formal subschemes $\\scrG$ of $\\scrD$ which lift $\\scrG_k$ and which have natural structures of formal Lie groups over $\\Spf(W(k))$ associated to $p$-divisible groups over $W(k)$. Applications to Traverso (ultimate) stratifications are included as well.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-15T15:51:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18",
      "14F30",
      "14G35",
      "14L05",
      "20G25"
    ],
    "keywords": [
      "p-divisible groups",
      "formal lie groups",
      "deformation subspaces",
      "formal deformation space",
      "construct formal subschemes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7508V"
    }
  }
}