{
  "id": "1712.03187",
  "version": "v1",
  "published": "2017-12-08T17:21:23.000Z",
  "updated": "2017-12-08T17:21:23.000Z",
  "title": "The non-nil-invariance of TP",
  "authors": [
    "Ryo Horiuchi"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AT",
    "math.KT",
    "math.NT"
  ],
  "abstract": "Hesselholt defined a spectrum $\\operatorname{TP}(X)$, called periodic topological cyclic homology, for a scheme $X$ using topological Hochshild homology and the Tate construction, which is a topological analogue of the Connes-Tsygan periodic cyclic homology $\\operatorname{HP}$ defined by Hochschild homology and the Tate construction. Goodwillie proved that for $R$ an algebra over a field of characteristic 0 and $I$ a nilpotent ideal of $R$, the quotient map $R\\to R/I$ induces an isomorphim on $\\rm HP$. In this article, we show that the analogous result for $\\rm TP$ does not hold, that is, there is an algebra of positive characteristic and a nilpotent ideal such that the quotient map does not induce an isomorphism on $\\operatorname{TP}$, even rationally.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-08T17:21:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotent ideal",
      "non-nil-invariance",
      "quotient map",
      "connes-tsygan periodic cyclic homology",
      "tate construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}