{
  "id": "math/0511534",
  "version": "v1",
  "published": "2005-11-21T23:15:25.000Z",
  "updated": "2005-11-21T23:15:25.000Z",
  "title": "The generating hypothesis in the derived category of R-modules",
  "authors": [
    "Keir H. Lockridge"
  ],
  "comment": "16 pages, submitted to JPAA",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper, we prove a version of Freyd's generating hypothesis for triangulated categories: if D is a cocomplete triangulated category and S is an object in D whose endomorphism ring is graded commutative and concentrated in degree zero, then S generates (in the sense of Freyd) the thick subcategory determined by S if and only if the endomorphism ring of S is von Neumann regular. As a corollary, we obtain that the generating hypothesis is true in the derived category of a commutative ring R if and only if R is von Neumann regular. We also investigate alternative formulations of the generating hypothesis in the derived category. Finally, we give a characterization of the Noetherian stable homotopy categories in which the generating hypothesis is true.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-21T23:15:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived category",
      "von neumann regular",
      "noetherian stable homotopy categories",
      "endomorphism ring",
      "degree zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11534L"
    }
  }
}