{
  "id": "2311.12254",
  "version": "v1",
  "published": "2023-11-21T00:26:38.000Z",
  "updated": "2023-11-21T00:26:38.000Z",
  "title": "A Counterexample to a Question on Grothendieck Groups of Schemes",
  "authors": [
    "Amal Mattoo"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "If an element of the Grothendieck group of the derived category of a scheme is locally represented by perfect complexes, then can the original element be represented by a perfect complex? We provide a counterexample on a projective variety of dimension 2, as well as a counterexample on a thickening of a Dedekind domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-21T00:26:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F08",
      "19A99",
      "13D15"
    ],
    "keywords": [
      "grothendieck group",
      "counterexample",
      "perfect complex",
      "dedekind domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}