{
  "id": "2108.09492",
  "version": "v1",
  "published": "2021-08-21T11:16:52.000Z",
  "updated": "2021-08-21T11:16:52.000Z",
  "title": "Local Solubility of Hyperelliptic Curves",
  "authors": [
    "Omri Faraggi"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a condition for a hyperelliptic curve $C$ over a local field $K$ to be locally soluble, on the condition that $C$ obtains semistable reduction after a tame extension of $K$, and that the residue field $k$ is sufficiently large relative to the genus of the curve. The condition is presented in terms of the cluster picture of $C$, a combinatorial object which determines much of the local arithmetic of $C$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-21T11:16:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperelliptic curve",
      "local solubility",
      "local arithmetic",
      "tame extension",
      "local field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}