{
  "id": "2103.11837",
  "version": "v1",
  "published": "2021-03-19T00:20:11.000Z",
  "updated": "2021-03-19T00:20:11.000Z",
  "title": "Properties of Breuil-Kisin modules inherited by $p$-divisible groups",
  "authors": [
    "Absos Ali Shaikh",
    "Mabud Ali Sarkar"
  ],
  "comment": "13 pages, we studied the properties of Breuil-Kisin modules and any comments regarding the work are mostly welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, by assuming a faithful action of a finite flat $\\mathbb{Z}_p$-algebra $\\mathscr{R}$ on a $p$-divisible group $\\mathcal{G}$ defined over the ring of $p$-adic integers $\\mathscr{O}_K$, we have constructed a new Breuil-Kisin module $\\mathfrak{M}$ defined over the ring $\\mathfrak{S}:=W(\\kappa)[[u]]$ and studied freeness and projectiveness properties of such a module. Finally we have lifted the Breuil-Kisin module to \\'etale level following the $\\mathscr{R}$-action and showed that if the $p$-adic Tate module of a $p$-divisible group $\\mathcal{G}$ over $\\mathscr{O}_K$ is free then the corresponding lifted Breuil-Kisin module is free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-19T00:20:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F85",
      "14L05"
    ],
    "keywords": [
      "divisible group",
      "adic tate module",
      "projectiveness properties",
      "adic integers",
      "corresponding lifted breuil-kisin module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}