{
  "id": "1411.3759",
  "version": "v1",
  "published": "2014-11-13T22:37:58.000Z",
  "updated": "2014-11-13T22:37:58.000Z",
  "title": "Finiteness of unramified deformation rings",
  "authors": [
    "Patrick B. Allen",
    "Frank Calegari"
  ],
  "comment": "To appear in Algebra & Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that the universal unramified deformation ring $R^{\\mathrm{unr}}$ of a continuous Galois representation $\\overline{\\rho}: G_{F^{+}} \\rightarrow \\mathrm{GL}_n(k)$ (for a totally real field $F^{+}$ and finite field $k$) is finite over $\\mathcal{O} = W(k)$ in many cases. We also prove (under similar hypotheses) that the universal deformation ring $R^{\\mathrm{univ}}$ is finite over the local deformation ring $R^{\\mathrm{loc}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-13T22:37:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F70"
    ],
    "keywords": [
      "finiteness",
      "continuous galois representation",
      "totally real field",
      "finite field",
      "similar hypotheses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.3759A"
    }
  }
}