{
  "id": "1003.3143",
  "version": "v1",
  "published": "2010-03-16T13:12:10.000Z",
  "updated": "2010-03-16T13:12:10.000Z",
  "title": "Deformation rings which are not local complete intersections",
  "authors": [
    "Frauke M. Bleher",
    "Ted Chinburg",
    "Bart de Smit"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the inverse problem for the versal deformation rings $R(\\Gamma,V)$ of finite dimensional representations $V$ of a finite group $\\Gamma$ over a field $k$ of positive characteristic $p$. This problem is to determine which complete local commutative Noetherian rings with residue field $k$ can arise up to isomorphism as such $R(\\Gamma,V)$. We show that for all integers $n \\ge 1$ and all complete local commutative Noetherian rings $\\mathcal{W}$ with residue field $k$, the ring $\\mathcal{W}[[t]]/(p^n t,t^2)$ arises in this way. This ring is not a local complete intersection if $p^n\\mathcal{W}\\neq\\{0\\}$, so we obtain an answer to a question of M. Flach in all characteristics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-16T13:12:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11R32",
      "20C20",
      "11R29"
    ],
    "keywords": [
      "local complete intersection",
      "complete local commutative noetherian rings",
      "residue field",
      "finite dimensional representations",
      "versal deformation rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3143B"
    }
  }
}