{
  "id": "math/0311368",
  "version": "v1",
  "published": "2003-11-21T01:04:18.000Z",
  "updated": "2003-11-21T01:04:18.000Z",
  "title": "On the Ramification of Hecke Algebras at Eisenstein Primes",
  "authors": [
    "Frank Calegari",
    "Matthew Emerton"
  ],
  "comment": "39 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using the modularity technique of Wiles, we study the Hecke algebra of weight 2 and prime level N localized at the Eisenstein primes. On the way, we recover some results of Mazur (\"Modular Curves and the Eisenstein Ideal\") from a deformation theoretic point of view. Combining some of our results with a theorem of Merel, we obtain new information about the p-part of the class groups of Q(N^(1/p)), where p and N are prime, and N = 1 mod p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-21T01:04:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11R29"
    ],
    "keywords": [
      "eisenstein primes",
      "hecke algebra",
      "ramification",
      "deformation theoretic point",
      "class groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11368C"
    }
  }
}