{
  "id": "1104.2858",
  "version": "v1",
  "published": "2011-04-14T18:20:38.000Z",
  "updated": "2011-04-14T18:20:38.000Z",
  "title": "On the center of the ring of differential operators on a smooth variety over $\\bZ/p^n\\bZ$",
  "authors": [
    "Allen Stewart",
    "Vadim Vologodsky"
  ],
  "comment": "16 pages",
  "doi": "10.1112/S0010437X12000462",
  "categories": [
    "math.AG"
  ],
  "abstract": "We compute the center of the ring of PD differential operators on a smooth variety over $\\bZ/p^n\\bZ$ confirming a conjecture of Kaledin. More generally, given an associative algebra $A_0$ over $\\bF_p$ and its flat deformation $A_n$ over $\\bZ/p^{n+1}\\bZ$ we prove that under a certain non-degeneracy condition the center of $A_n$ is isomorphic to the ring of length $n+1$ Witt vectors over the center of $A_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-14T18:20:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10",
      "14G17",
      "16S34",
      "16S80"
    ],
    "keywords": [
      "smooth variety",
      "pd differential operators",
      "flat deformation",
      "non-degeneracy condition",
      "witt vectors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.2858S"
    }
  }
}