{
  "id": "1202.5147",
  "version": "v2",
  "published": "2012-02-23T10:48:16.000Z",
  "updated": "2014-10-04T11:03:19.000Z",
  "title": "Tensor functors between categories of quasi-coherent sheaves",
  "authors": [
    "Martin Brandenburg",
    "Alexandru Chirvasitu"
  ],
  "comment": "22 pages; revised version",
  "journal": "J. Algebra 399 (2014), 675-692",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X and the category of cocontinuous tensor functors Qcoh(X) --> Qcoh(Y). This is an improvement of a result by Lurie and may be interpreted as the statement that algebraic geometry is 2-affine. Moreover, we prove the analogous version of this result for Durov's notion of generalized schemes over F_1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-23T10:48:16.000Z",
      "abstract": "For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X and the category of cocontinuous tensor functors Qcoh(X) --> Qcoh(Y). This is an improvement of a result by Lurie and may be interpreted as the statement that algebraic geometry is 2-affine. Moreover, we prove the analogous version of this result for Durov's notion of generalized schemes.",
      "comment": "21 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-04T11:03:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-coherent sheaves",
      "pullback construction implements",
      "cocontinuous tensor functors qcoh",
      "quasi-compact quasi-separated scheme",
      "discrete category"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5147B"
    }
  }
}