{
  "id": "math/0308202",
  "version": "v5",
  "published": "2003-08-20T21:17:33.000Z",
  "updated": "2012-01-24T15:26:04.000Z",
  "title": "A motivic conjecture of Milne",
  "authors": [
    "Adrian Vasiu"
  ],
  "comment": "60 pages. Final version to appear in J. Reine Agew. Math. (Crelle)",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let k be an algebraically closed field of characteristic p>0. Let W(k) be the ring of Witt vectors with coefficients in k. We prove a motivic conjecture of Milne that relates, in the case of abelian schemes, the \\'etale cohomology with $\\dbZ_p$ coefficients to the crystalline cohomology with integral coefficients, in the more general context of p-divisible groups endowed with {\\it arbitrary} families of crystalline tensors over a finite, discrete valuation ring extension of W(k). This extends a result of Faltings in [Fa2]. As a main new tool we construct global deformations of p-divisible groups endowed with crystalline tensors over certain regular, formally smooth schemes over W(k) whose special fibers over k have a Zariski dense set of k-valued points.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-01-24T15:26:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18",
      "11S25",
      "14F30",
      "14G35",
      "14L05",
      "20G25"
    ],
    "keywords": [
      "motivic conjecture",
      "crystalline tensors",
      "p-divisible groups",
      "coefficients",
      "discrete valuation ring extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......8202V"
    }
  }
}