{
  "id": "2410.20262",
  "version": "v1",
  "published": "2024-10-26T19:40:15.000Z",
  "updated": "2024-10-26T19:40:15.000Z",
  "title": "Supersingular curves of genus five for primes congruent to three modulo four",
  "authors": [
    "Jeremy Booher",
    "Rachel Pries"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For every prime number $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. This extends earlier work of Ekedahl and of Harashita, Kudo, and Senda.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-26T19:40:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11M38",
      "14G10",
      "14H10",
      "14H40",
      "11G10",
      "14G15",
      "14H37",
      "14H30"
    ],
    "keywords": [
      "primes congruent",
      "supersingular curves",
      "extends earlier work",
      "smooth curve",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}