{
  "id": "0709.3905",
  "version": "v2",
  "published": "2007-09-25T10:04:42.000Z",
  "updated": "2008-10-27T13:07:21.000Z",
  "title": "On Voevodsky's algebraic K-theory spectrum BGL",
  "authors": [
    "I. Panin",
    "K. Pimenov",
    "O. Röndigs"
  ],
  "comment": "LaTeX, 49 pages, uses XY-pic. Several changes. To appear in: The Abel symposium 2007",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "Under a certain normalization assumption we prove that the $\\Pro^1$-spectrum $\\mathrm{BGL}$ of Voevodsky which represents algebraic $K$-theory is unique over $\\Spec(\\mathbb{Z})$. Following an idea of Voevodsky, we equip the $\\Pro^1$-spectrum $\\mathrm{BGL}$ with the structure of a commutative $\\Pro^1$-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over $\\Spec(\\mathbb{Z})$. For an arbitrary Noetherian scheme $S$ of finite Krull dimension we pull this structure back to obtain a distinguished monoidal structure on $\\mathrm{BGL}$. This monoidal structure is relevant for our proof of the motivic Conner-Floyd theorem. It has also been used by Gepner and Snaith to obtain a motivic version of Snaith's theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-27T13:07:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19E08",
      "55P43"
    ],
    "keywords": [
      "voevodskys algebraic k-theory spectrum bgl",
      "monoidal structure",
      "normalization assumption",
      "motivic conner-floyd theorem",
      "motivic stable homotopy category"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.3905P"
    }
  }
}