{
  "id": "0904.0227",
  "version": "v4",
  "published": "2009-04-01T18:26:28.000Z",
  "updated": "2014-09-18T13:47:00.000Z",
  "title": "Noetherian approximation of algebraic spaces and stacks",
  "authors": [
    "David Rydh"
  ],
  "comment": "39 pages; complete overhaul of paper; generalized results and simplified proofs (no groupoid-calculations); added more applications and appendices with standard results on constructible properties and limits for stacks; generalized Thm C (no finite presentation hypothesis); some minor changes in 2,1-2.8, 8.2, 8.8 and 8.9; final version",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that every scheme/algebraic space/stack that is quasi-compact with quasi-finite diagonal can be approximated by a noetherian scheme/algebraic space/stack. More generally, we show that any stack which is etale-locally a global quotient stack can be approximated. Examples of applications are generalizations of Chevalley's, Serre's and Zariski's theorems and Chow's lemma to the non-noetherian setting. We also show that every quasi-compact algebraic stack with quasi-finite diagonal has a finite generically flat cover by a scheme.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-10T17:20:22.000Z",
      "comment": "38 pages; complete overhaul of paper; generalized results and simplified proofs (no groupoid-calculations); added more applications and appendices with standard results on constructible properties and limits for stacks; generalized Thm C (no finite presentation hypothesis)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-18T13:47:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A20"
    ],
    "keywords": [
      "algebraic spaces",
      "noetherian approximation",
      "quasi-finite diagonal",
      "global quotient stack",
      "noetherian scheme/algebraic space/stack"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0227R"
    }
  }
}