{
  "id": "1502.02190",
  "version": "v1",
  "published": "2015-02-07T22:39:02.000Z",
  "updated": "2015-02-07T22:39:02.000Z",
  "title": "The Chromatic Splitting Conjecture at n=p=2",
  "authors": [
    "Agnes Beaudry"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We show that the strongest form of Hopkins' chromatic splitting conjecture, as stated by Hovey, cannot hold at chromatic level n=2 at the prime p=2. More precisely, for V(0) the mod 2 Moore spectrum, we prove that the k'th homotopy group of L_1L_{K(2)}V(0) is not zero when k is congruent to 5 modulo 8. We explain how this contradicts the decomposition of L_1L_{K(2)}S predicted by the chromatic splitting conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-07T22:39:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q45",
      "55P60"
    ],
    "keywords": [
      "chromatic splitting conjecture",
      "kth homotopy group",
      "strongest form",
      "moore spectrum",
      "chromatic level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150202190B"
    }
  }
}