{
  "id": "1905.10495",
  "version": "v1",
  "published": "2019-05-25T01:44:25.000Z",
  "updated": "2019-05-25T01:44:25.000Z",
  "title": "Canonical lifts and $δ$-structures",
  "authors": [
    "James Borger",
    "Lance Gurney"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We extend the Serre-Tate theory of canonical lifts of ordinary abelian varieties to arbitrary families of ordinary abelian varieties parameterised by a $p$-adic formal scheme $S$. We show that the canonical lift is the unique lift to $W(S)$ which admits a $\\delta$-structure in the sense of Joyal and Buium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-25T01:44:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "canonical lift",
      "ordinary abelian varieties",
      "adic formal scheme",
      "serre-tate theory",
      "unique lift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}