{
  "id": "1605.04535",
  "version": "v1",
  "published": "2016-05-15T12:50:28.000Z",
  "updated": "2016-05-15T12:50:28.000Z",
  "title": "A^1-connectedness in reductive algebraic groups",
  "authors": [
    "Chetan Balwe",
    "Anand Sawant"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG",
    "math.GR",
    "math.KT"
  ],
  "abstract": "Using sheaves of A^1-connected components, we prove that the Morel-Voevodsky singular construction on a reductive algebraic group fails to be A^1-local if the group does not satisfy suitable isotropy hypotheses. As a consequence, we show the failure of A^1-invariance of torsors for such groups on smooth affine schemes over infinite perfect fields. We also characterize A^1-connected reductive algebraic groups over an infinite perfect field and use this characterization to study relationship of A^1-connectedness with R-equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-15T12:50:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F42"
    ],
    "keywords": [
      "infinite perfect field",
      "morel-voevodsky singular construction",
      "smooth affine schemes",
      "reductive algebraic group fails",
      "satisfy suitable isotropy hypotheses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}