{
  "id": "2205.07801",
  "version": "v1",
  "published": "2022-05-16T16:47:20.000Z",
  "updated": "2022-05-16T16:47:20.000Z",
  "title": "Large rank jumps on elliptic surfaces and the Hilbert property",
  "authors": [
    "Renato Dias Costa",
    "Cecília Salgado"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Given a rational elliptic surface over a number field, we study the collection of fibers whose Mordell--Weil rank is greater than the generic rank. We give conditions on the singular fibers to assure that the collection of fibers for which the rank jumps of at least 3 is not thin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-16T16:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "14J27",
      "11G05"
    ],
    "keywords": [
      "large rank jumps",
      "hilbert property",
      "rational elliptic surface",
      "number field",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}