{
  "id": "2007.01749",
  "version": "v1",
  "published": "2020-07-03T15:14:17.000Z",
  "updated": "2020-07-03T15:14:17.000Z",
  "title": "A user's guide to the local arithmetic of hyperelliptic curves",
  "authors": [
    "Alex J. Best",
    "L. Alexander Betts",
    "Matthew Bisatt",
    "Raymond van Bommel",
    "Vladimir Dokchitser",
    "Omri Faraggi",
    "Sabrina Kunzweiler",
    "Céline Maistret",
    "Adam Morgan",
    "Simone Muselli",
    "Sarah Nowell"
  ],
  "comment": "38 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous papers have used this machinery of \"cluster pictures\" to compute a plethora of arithmetic invariants associated to these curves. The purpose of this user's guide is to summarise and centralise all of these results in a self-contained fashion, complemented by an abundance of examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-03T15:14:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11G10",
      "14D10",
      "14G20",
      "14H45",
      "14Q05"
    ],
    "keywords": [
      "hyperelliptic curves",
      "users guide",
      "local arithmetic",
      "odd residue characteristic",
      "cluster pictures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}