{
  "id": "2310.11337",
  "version": "v1",
  "published": "2023-10-17T15:15:03.000Z",
  "updated": "2023-10-17T15:15:03.000Z",
  "title": "On the Northcott property for infinite extensions",
  "authors": [
    "Martin Widmer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We start with a brief survey on the Northcott property for subfields of the algebraic numbers $\\Qbar$. Then we introduce a new criterion for its validity (refining the author's previous criterion), addressing a problem of Bombieri. We show that Bombieri and Zannier's theorem, stating that the maximal abelian extension of a number field $K$ contained in $K^{(d)}$ has the Northcott property, follows very easily from this refined criterion. Here $K^{(d)}$ denotes the composite field of all extensions of $K$ of degree at most $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-17T15:15:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11G50",
      "11R06",
      "11R20",
      "37P30"
    ],
    "keywords": [
      "northcott property",
      "infinite extensions",
      "maximal abelian extension",
      "brief survey",
      "algebraic numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}