{
  "id": "2301.06818",
  "version": "v1",
  "published": "2023-01-17T11:36:54.000Z",
  "updated": "2023-01-17T11:36:54.000Z",
  "title": "Indecomposability of derived categories for arbitrary schemes",
  "authors": [
    "Ana Cristina López Martín",
    "Fernando Sancho de Salas"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal decompositions that are linear over the base. These criteria are based on the base loci of the global or relative dualizing complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-17T11:36:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "14F05",
      "18E25",
      "14H52"
    ],
    "keywords": [
      "arbitrary schemes",
      "derived category",
      "indecomposability",
      "smooth projective variety",
      "semiorthogonal decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}