{
  "id": "1805.04585",
  "version": "v1",
  "published": "2018-05-11T20:42:22.000Z",
  "updated": "2018-05-11T20:42:22.000Z",
  "title": "Modules, fields of definition, and the Culler-Shalen norm",
  "authors": [
    "Charles Katerba"
  ],
  "comment": "17 pages. Comments are very welcome and appreciated",
  "categories": [
    "math.GT"
  ],
  "abstract": "Culler-Shalen theory uses the algebraic geometry of the SL(2,C)-character variety of a 3-manifold to construct essential surfaces in the manifold. There are module structures associated to the coordinate rings of the irreducible components of character varieties that are intimately related to essential surface construction. When these modules are finitely generated, we derive a formula for their rank that incorporates the irreducible component's field of definition and the Culler-Shalen norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-11T20:42:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "culler-shalen norm",
      "definition",
      "construct essential surfaces",
      "essential surface construction",
      "module structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}