{
  "id": "1906.00921",
  "version": "v1",
  "published": "2019-06-03T16:47:24.000Z",
  "updated": "2019-06-03T16:47:24.000Z",
  "title": "Automorphisms of categories of schemes",
  "authors": [
    "Remy van Dobben de Bruyn"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "Given two schemes $S$ and $S'$, we prove that every equivalence between $\\mathbf{Sch}_S$ and $\\mathbf{Sch}_{S'}$ comes from a unique isomorphism between $S$ and $S'$. This eliminates all Noetherian and finite type hypotheses from a result of Mochizuki and fully answers a programme set out by Brandenburg in a series of questions on MathOverflow in 2011.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T16:47:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A15",
      "18B99",
      "14J50"
    ],
    "keywords": [
      "automorphisms",
      "categories",
      "finite type hypotheses",
      "unique isomorphism",
      "programme set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}