{
  "id": "1801.08471",
  "version": "v1",
  "published": "2018-01-25T16:16:18.000Z",
  "updated": "2018-01-25T16:16:18.000Z",
  "title": "Affine Grassmannians in A^1-algebraic topology",
  "authors": [
    "Tom Bachmann"
  ],
  "comment": "10 pages; comments welcome!",
  "categories": [
    "math.AG",
    "math.AT",
    "math.KT"
  ],
  "abstract": "Let k be a field. Denote by Spc(k)_* the unstable, pointed motivic homotopy category and by Omega_Gm: Spc(k)_* \\to Spc(k)_* the Gm-loops functor. For a k-group G, denote by Gr_G the affine Grassmannian of G. If k is infinite and G is split reductive, we provide a canonical motivic equivalence Omega_Gm G = Gr_G. If k satisfies resolution of singularities, we use this to compute the motive M(Omega_Gm G) in DM(k, Z).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-25T16:16:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine grassmannian",
      "pointed motivic homotopy category",
      "gm-loops functor",
      "satisfies resolution",
      "canonical motivic equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}