{
  "id": "1312.4822",
  "version": "v1",
  "published": "2013-12-17T15:22:09.000Z",
  "updated": "2013-12-17T15:22:09.000Z",
  "title": "Néron models of algebraic curves",
  "authors": [
    "Qing Liu",
    "Jilong Tong"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let S be a Dedekind scheme with field of functions K. We show that if X_K is a smooth connected proper curve of positive genus over K, then it admits a N\\'eron model over S, i.e., a smooth separated model of finite type satisfying the usual N\\'eron mapping property. It is given by the smooth locus of the minimal proper regular model of X_K over S, as in the case of elliptic curves. When S is excellent, a similar result holds for connected smooth affine curves different from the affine line, with locally finite type N\\'eron models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-17T15:22:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H25",
      "14G20",
      "14G40",
      "11G35"
    ],
    "keywords": [
      "algebraic curves",
      "néron models",
      "locally finite type neron models",
      "minimal proper regular model",
      "smooth connected proper curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4822L"
    }
  }
}