{
  "id": "math/0403285",
  "version": "v1",
  "published": "2004-03-17T11:49:31.000Z",
  "updated": "2004-03-17T11:49:31.000Z",
  "title": "A Hilbert-Kunz criterion for solid closure in dimension two (characteristic zero)",
  "authors": [
    "Holger Brenner"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AC"
  ],
  "abstract": "Let I denote a homogeneous R_+-primary ideal in a two-dimensional normal standard-graded domain over an algebraically closed field of characteristic zero. We show that a homogeneous element f belongs to the solid closure I^* if and only if e_{HK}(I) = e_{HK}((I,f)), where e_{HK} denotes the (characteristic zero) Hilbert-Kunz multiplicity of an ideal. This provides a version in characteristic zero of the well-known Hilbert-Kunz criterion for tight closure in positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-17T11:49:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A35",
      "13D40",
      "14H60"
    ],
    "keywords": [
      "characteristic zero",
      "solid closure",
      "well-known hilbert-kunz criterion",
      "two-dimensional normal standard-graded domain",
      "tight closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3285B"
    }
  }
}