{
  "id": "1111.4664",
  "version": "v5",
  "published": "2011-11-20T19:01:25.000Z",
  "updated": "2013-02-13T20:58:09.000Z",
  "title": "Homotopy invariance of non-stable K_1-functors",
  "authors": [
    "Anastasia Stavrova"
  ],
  "comment": "40 pages (font size enlarged)",
  "categories": [
    "math.AG",
    "math.GR",
    "math.KT"
  ],
  "abstract": "Let G be reductive algebraic group over a field k, such that every semisimple normal subgroup of G has isotropic rank >=2. Let K_1^G be the non-stable K_1-functor associated to G (also called the Whitehead group of G in the field case). We show that K_1^G(k)=K_1^G(k[X_1,...,X_n]) for any n>= 1. This implies that K_1^G is A^1-homotopy invariant on the category of regular k-algebras, if k is perfect. If k is infinite perfect, one also deduces that K_1^G(R)-> K_1^G(K) is injective for any regular local k-algebra R with the fraction field K.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-02-13T20:58:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19B99",
      "20G07",
      "20G15",
      "20G35"
    ],
    "keywords": [
      "homotopy invariance",
      "non-stable",
      "regular local k-algebra",
      "semisimple normal subgroup",
      "fraction field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4664S"
    }
  }
}