{
  "id": "2103.06917",
  "version": "v1",
  "published": "2021-03-11T19:29:51.000Z",
  "updated": "2021-03-11T19:29:51.000Z",
  "title": "Néron models of Jacobians over bases of arbitrary dimension",
  "authors": [
    "Thibault Poiret"
  ],
  "comment": "37 pages including bibliography. Comments are welcome",
  "categories": [
    "math.AG",
    "math.AC",
    "math.NT"
  ],
  "abstract": "We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models relate to each other. We construct a N\\'eron model for the Jacobian of $X_U$, and describe it locally on $S$ as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the N\\'eron model to be separated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T19:29:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary dimension",
      "néron models",
      "neron model",
      "well-chosen nodal model",
      "nodal reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}