{
  "id": "1202.5085",
  "version": "v3",
  "published": "2012-02-23T04:46:11.000Z",
  "updated": "2012-06-10T09:57:44.000Z",
  "title": "Universality of the category of schemes",
  "authors": [
    "Satoshi Takagi"
  ],
  "comment": "37 pages, revised June. 10, 2012",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "In this paper, we generalize the construction method of schemes to other algebraic categories, and show that the category of coherent schemes can be characterized by a universal property, if we fix the class of Grothendieck topology. Also, we introduce the notion of $\\scr{C}$-schemes, which is a further generalization of coherent schemes and still shares common properties with ordinary schemes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-10T09:57:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A15",
      "14T05"
    ],
    "keywords": [
      "universality",
      "coherent schemes",
      "shares common properties",
      "construction method",
      "grothendieck topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5085T"
    }
  }
}