{
  "id": "1708.06599",
  "version": "v1",
  "published": "2017-08-22T13:37:56.000Z",
  "updated": "2017-08-22T13:37:56.000Z",
  "title": "Three counterexamples concerning the Northcott property of fields",
  "authors": [
    "Arno Fehm"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give three examples of fields concerning the Northcott property on elements of small height: The first one has the Northcott property but its Galois closure does not satisfy the Bogomolov property. The second one has the Northcott property and is pseudo-algebraically closed, i.e. every variety has a dense set of rational points. The third one has bounded local degree at infinitely many rational primes but does not have the Northcott property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-22T13:37:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "12E25",
      "12F10"
    ],
    "keywords": [
      "northcott property",
      "counterexamples concerning",
      "small height",
      "galois closure",
      "bogomolov property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}