{
  "id": "1612.06456",
  "version": "v1",
  "published": "2016-12-19T23:35:33.000Z",
  "updated": "2016-12-19T23:35:33.000Z",
  "title": "Serre-Tate theory for Shimura varieties of Hodge type",
  "authors": [
    "Ananth N. Shankar",
    "Rong Zhou"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the formal neighbourhood of a point in $\\mu$-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a shifted cascade. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization in terms of its endomorphisms in analogy with the Serre-Tate canonical lift of an ordinary abelian variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-19T23:35:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "serre-tate theory",
      "formal neighbourhood",
      "hodge type shimura variety",
      "ordinary abelian variety",
      "shifted cascade corresponds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}