{
  "id": "2108.05235",
  "version": "v1",
  "published": "2021-08-11T14:08:22.000Z",
  "updated": "2021-08-11T14:08:22.000Z",
  "title": "Geometric quadratic Chabauty over number fields",
  "authors": [
    "Pavel Čoupek",
    "David T. -B. G. Lilienfeldt",
    "Zijian Yao",
    "Luciena Xiao Xiao"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "This article generalizes the geometric quadratic Chabauty method, initiated over $\\mathbb{Q}$ by Edixhoven and Lido, to curves defined over arbitrary number fields. The main result is a conditional bound on the number of rational points on curves that satisfy an additional Chabauty type condition on the Mordell-Weil rank of the Jacobian. The method gives a more direct approach to the generalization by Dogra of the quadratic Chabauty method to arbitrary number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-11T14:08:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G30",
      "11D45",
      "14G05"
    ],
    "keywords": [
      "arbitrary number fields",
      "geometric quadratic chabauty method",
      "additional chabauty type condition",
      "direct approach",
      "conditional bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}