{
  "id": "1103.2333",
  "version": "v2",
  "published": "2011-03-11T18:30:18.000Z",
  "updated": "2012-01-31T20:30:18.000Z",
  "title": "Abelian Varieties and Galois Extensions of Hilbertian Fields",
  "authors": [
    "Christopher Thornhill"
  ],
  "comment": "10 pages; revision; typos corrected; clarified ambiguities; changed numbering/naming of results; Prop. 2 replaced by Lemmas 6-11; some definitions altered to simplify presentation; small changes made to some proofs to correct errors (notably Props. 12 and 24); changes made to some proofs and results added to simplify/streamline arguments (notably Lemmas 9 and 15); new \"thank you's\" added",
  "categories": [
    "math.NT"
  ],
  "abstract": "In a recent paper, Moshe Jarden proposed a conjecture, later named the Kuykian conjecture, which states that if A is an abelian variety defined over a Hilbertian field K, then every intermediate field of K(A_{tor})/K is Hilbertian. We prove that the conjecture holds for Galois extensions of K in K(A_{tor}).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-31T20:30:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12E25",
      "12E30"
    ],
    "keywords": [
      "galois extensions",
      "hilbertian field",
      "intermediate field",
      "moshe jarden",
      "kuykian conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2333T"
    }
  }
}