{
  "id": "1211.6357",
  "version": "v2",
  "published": "2012-11-27T16:48:21.000Z",
  "updated": "2013-04-13T10:48:56.000Z",
  "title": "Moduli of p-divisible groups",
  "authors": [
    "Peter Scholze",
    "Jared Weinstein"
  ],
  "comment": "74 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of p-adic Hodge theory. This allows us to formulate and prove duality isomorphisms between basic Rapoport-Zink spaces at infinite level in general. Moreover, we identify the image of the period morphism, reproving results of Faltings. For this, we give a general classification of p-divisible groups over the ring of integers of a complete algebraically closed field in the spirit of Riemann's classification of complex abelian varieties. Another key ingredient is a full faithfulness result for the Dieudonn\\'e module functor for p-divisible groups over semiperfect rings (meaning rings on which the Frobenius map is surjective).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-13T10:48:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L05",
      "14G22"
    ],
    "keywords": [
      "p-divisible groups",
      "infinite level",
      "p-adic hodge theory",
      "full faithfulness result",
      "complex abelian varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 74,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6357S"
    }
  }
}