{
  "id": "2305.15874",
  "version": "v1",
  "published": "2023-05-25T09:10:26.000Z",
  "updated": "2023-05-25T09:10:26.000Z",
  "title": "Normal distribution of bad reduction",
  "authors": [
    "Robert J. Lemke Oliver",
    "Daniel Loughran",
    "Ari Shnidman"
  ],
  "comment": "12 pages, comments welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, $100\\%$ of curves in these families have, in a precise sense, many such primes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-25T09:10:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G30",
      "60F05"
    ],
    "keywords": [
      "bad reduction",
      "normal distribution laws",
      "precise sense",
      "bad semistable reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}