{
  "id": "1404.4549",
  "version": "v4",
  "published": "2014-04-17T14:59:23.000Z",
  "updated": "2014-09-11T03:46:43.000Z",
  "title": "A Sheaf Model of the Algebraic Closure",
  "authors": [
    "Bassel Mannaa",
    "Thierry Coquand"
  ],
  "comment": "In Proceedings CL&C 2014, arXiv:1409.2593",
  "journal": "EPTCS 164, 2014, pp. 18-32",
  "doi": "10.4204/EPTCS.164.2",
  "categories": [
    "math.LO"
  ],
  "abstract": "In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an algebraic closure. One can then extract computational content from this model. We give examples of computation based on this model.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-01T15:25:36.000Z",
      "title": "A Sheaf Model Of The Algebraic Closure",
      "abstract": "In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field $K$. This poses some problems to showing the existence of the algebraic closure of $K$. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic $0$ by building, in a constructive metatheory, a suitable site model where there is such an algebraic closure. One can then extract computational content from this model. We give examples of computation based on this model.",
      "comment": "17 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-11T03:46:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F55",
      "03G30",
      "12Y05",
      "F.4.1"
    ],
    "keywords": [
      "algebraic closure",
      "sheaf model",
      "extract computational content",
      "general decide",
      "suitable site model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4549M"
    }
  }
}