{
  "id": "2212.01138",
  "version": "v1",
  "published": "2022-12-02T12:36:14.000Z",
  "updated": "2022-12-02T12:36:14.000Z",
  "title": "The Hilbert property for arithmetic schemes",
  "authors": [
    "Cedric Luger"
  ],
  "comment": "10 pages, accepted for publication in Acta Arithmetica",
  "categories": [
    "math.AG"
  ],
  "abstract": "We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of Bary-Soroker-Fehm-Petersen and Corvaja-Zannier by proving several structure results related to products and finite \\'{e}tale covers of arithmetic schemes with the Hilbert property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-02T12:36:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G99",
      "14G05",
      "14G40"
    ],
    "keywords": [
      "arithmetic schemes",
      "usual hilbert property",
      "integral domains",
      "near-integral points",
      "structure results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}