{
  "id": "2301.11193",
  "version": "v1",
  "published": "2023-01-26T16:04:47.000Z",
  "updated": "2023-01-26T16:04:47.000Z",
  "title": "Linear and quadratic Chabauty for affine hyperbolic curves",
  "authors": [
    "Marius Leonhardt",
    "Martin Lüdtke",
    "J. Steffen Müller"
  ],
  "comment": "19 pages; comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth $\\leq 2$ quotients of the fundamental group, following a construction of Balakrishnan-Dogra in the projective case. We also apply Betts' machinery of weight filtrations to give unconditional explicit upper bounds on the number of S-integral points when our conditions are satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-26T16:04:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G30",
      "11D45"
    ],
    "keywords": [
      "affine hyperbolic curves",
      "quadratic chabauty",
      "unconditional explicit upper bounds",
      "quadratic refined chabauty-kim loci",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}