{
  "id": "2211.01690",
  "version": "v1",
  "published": "2022-11-03T10:21:56.000Z",
  "updated": "2022-11-03T10:21:56.000Z",
  "title": "Regular models of modular curves in prime level over ${\\mathbb Z}_p^{\\mathrm{ur}}$",
  "authors": [
    "Bas Edixhoven",
    "Pierre Parent"
  ],
  "comment": "While this work was in progress, B. E. passed away, on January 16, 2022. He is deeply missed. (P. P.)",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give regular models for modular curves associated with (normalizer of) split and non-split Cartan subgroups of ${\\mathrm{GL}}_2 ({\\mathbb F}_p )$ (for $p$ any prime, $p\\ge 5$). We then compute the group of connected components of the fiber at $p$ of the N\\'eron model of their Jacobians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-03T10:21:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "11G20",
      "14G35"
    ],
    "keywords": [
      "modular curves",
      "regular models",
      "prime level",
      "non-split cartan subgroups",
      "neron model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}