{
  "id": "1309.0135",
  "version": "v1",
  "published": "2013-08-31T17:06:01.000Z",
  "updated": "2013-08-31T17:06:01.000Z",
  "title": "Ramification of local rings along valuations",
  "authors": [
    "Steven Dale Cutkosky",
    "Pham An Vinh"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AC"
  ],
  "abstract": "In this paper we discuss stable forms of extensions of algebraic local rings along a valuation in all dimensions over a field k of characteristic zero, and generalize a formula of Ghezzi, H\\`a and Kashcheyeva describing the extension of associated graded rings along the valuation for stable extensions of regular algebraic local rings of dimension two to arbitrary ground fields k of characteristic zero. We discuss the failure of this result in positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-31T17:06:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13B02"
    ],
    "keywords": [
      "characteristic zero",
      "ramification",
      "regular algebraic local rings",
      "arbitrary ground fields",
      "graded rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0135C"
    }
  }
}