{
  "id": "2005.10609",
  "version": "v1",
  "published": "2020-05-21T12:39:29.000Z",
  "updated": "2020-05-21T12:39:29.000Z",
  "title": "On the Northcott property and local degrees",
  "authors": [
    "Sara Checcoli",
    "Arno Fehm"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We construct infinite Galois extensions $K$ of $\\mathbb{Q}$ that satisfy the Northcott property on elements of small height, and where this property can be deduced solely from the splitting behavior of prime numbers in $K$. We also give examples of Galois extensions of $\\mathbb{Q}$ which have finite local degree at all prime numbers and do not satisfy the Northcott property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-21T12:39:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "12E30",
      "11R04",
      "12F05"
    ],
    "keywords": [
      "northcott property",
      "construct infinite galois extensions",
      "prime numbers",
      "finite local degree",
      "small height"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}