{
  "id": "1902.05666",
  "version": "v1",
  "published": "2019-02-15T03:04:23.000Z",
  "updated": "2019-02-15T03:04:23.000Z",
  "title": "On the mod-$p$ distribution of discriminants of $G$-extensions",
  "authors": [
    "Joachim König"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper was motivated by a recent paper by Krumm and Pollack investigating modulo-$p$ behaviour of quadratic twists with rational points of a given hyperelliptic curve, conditional on the abc-conjecture. We extend those results to twisted Galois covers with arbitrary Galois groups. The main point of this generalization is to interpret those results as statements about the sets of specializations of a given Galois cover under restrictions on the discriminant. In particular, we make a connection with existing heuristics about the distribution of discriminants of Galois extensions such as the Malle conjecture: our results show in a precise sense the non-existence of \"local obstructions\" to such heuristics, in many cases essentially only under the assumption that $G$ occurs as the Galois group of a Galois cover defined over $\\mathbb{Q}$. This complements and generalizes a similar result in the direction of the Malle conjecture by D\\`ebes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-15T03:04:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R32"
    ],
    "keywords": [
      "discriminant",
      "distribution",
      "malle conjecture",
      "arbitrary galois groups",
      "rational points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}