{
  "id": "1712.08004",
  "version": "v1",
  "published": "2017-12-20T15:10:27.000Z",
  "updated": "2017-12-20T15:10:27.000Z",
  "title": "Weak completions, bornologies and rigid cohomology",
  "authors": [
    "Guillermo Cortiñas",
    "Joachim Cuntz",
    "Ralf Meyer",
    "Georg Tamme"
  ],
  "comment": "14 pages. arXiv admin note: text overlap with arXiv:1708.00357",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $V$ be a complete discrete valuation ring with residue field $k$ of positive characteristic and with fraction field $K$ of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completion of a commutative $V$-algebra using completions of bornological $V$-algebras. This leads us to a functorial chain complex for a finitely generated commutative algebra over the residue field $k$ that computes its rigid cohomology in the sense of Berthelot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-20T15:10:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F30",
      "14F40",
      "13D03"
    ],
    "keywords": [
      "rigid cohomology",
      "weak completions",
      "bornologies",
      "residue field",
      "functorial chain complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}