{
  "id": "1710.06095",
  "version": "v1",
  "published": "2017-10-17T04:51:45.000Z",
  "updated": "2017-10-17T04:51:45.000Z",
  "title": "The action of the Hecke operators on the component groups of modular Jacobian varieties",
  "authors": [
    "Taekyung Kim",
    "Hwajong Yoo"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For a prime number $q\\geq 5$ and a positive integer $N$ prime to $q$, Ribet proved the action of the Hecke algebra on the component group of the Jacobian variety of the modular curve of level $Nq$ at $q$ is \"Eisenstein\", which means the Hecke operator $T_\\ell$ acts by $\\ell+1$ when $\\ell$ is a prime number not dividing the level. In this paper, we completely compute the action of the Hecke algebra on this component group by a careful study of supersingular points with extra automorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-17T04:51:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G18",
      "14G35"
    ],
    "keywords": [
      "jacobian variety",
      "modular jacobian varieties",
      "component group",
      "hecke operator",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}