{
  "id": "math/0602235",
  "version": "v2",
  "published": "2006-02-11T01:45:27.000Z",
  "updated": "2006-04-05T13:24:18.000Z",
  "title": "A criterion for regularity of local rings",
  "authors": [
    "Tom Bridgeland",
    "Srikanth Iyengar"
  ],
  "comment": "4 pages. Minor revisions. To appear in C. R. Acad. Sci. Paris, Ser. I",
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "abstract": "It is proved that a noetherian commutative local ring A containing a field is regular if there is a complex M of free A-modules with the following properties: M_i=0 for i not in [0,dim A]; the homology of M has finite length; H_0(M) contains the residue field of A as a direct summand. This result is an essential component in the proofs of the McKay correspondence in dimension 3 and of the statement that threefold flops induce equivalences of derived categories.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-05T13:24:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D22",
      "14E99"
    ],
    "keywords": [
      "regularity",
      "threefold flops induce equivalences",
      "mckay correspondence",
      "direct summand",
      "essential component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2235B"
    }
  }
}