{
  "id": "1509.06483",
  "version": "v1",
  "published": "2015-09-22T07:18:54.000Z",
  "updated": "2015-09-22T07:18:54.000Z",
  "title": "Néron models of $Pic^0$ via $Pic^0$",
  "authors": [
    "Alessandro Chiodo"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We provide a new description of the N\\'eron model of the Jacobian of a smooth curve $C_K$ with stable reduction $C_R$ on a discrete valuation ring $R$ with field of fractions $K$. Instead of the regular semistable model, our approach uses the regular twisted model, a twisted curve in the sense of Abramovich and Vistoli whose Picard functor contains a larger separated subgroup than the usual Picard functor of $C_R$. In this way, after extracting a suitable $l$th root from the uniformizer of $R$, the pullback of the N\\'eron model of the Jacobian represents a Picard functor $Pic^{0,l}$ of line bundles of degree zero on all irreducible components of a twisted curve. Over $R$, the group scheme $Pic^{0,l}$ descends to the N\\'eron model yielding a new geometric interpretation of its points and new combinatorial interpretations of the connected components of its special fibre. Furthermore, by construction, $Pic^{0,l}$ is represented by a universal group scheme $Pic^{0,l}_{g}$ of line bundles of degree zero over a smooth compactification $\\overline{M}_g^l$ of $M_g$ where all N\\'eron models of smoothings of stable curves are cast together after base change.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-22T07:18:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10"
    ],
    "keywords": [
      "néron models",
      "neron model",
      "degree zero",
      "line bundles",
      "twisted curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906483C"
    }
  }
}