{
  "id": "1005.1662",
  "version": "v6",
  "published": "2010-05-10T20:18:14.000Z",
  "updated": "2011-05-31T08:45:55.000Z",
  "title": "Some properties of Lubin-Tate cohomology for classifying spaces of finite groups",
  "authors": [
    "Andrew Baker",
    "Birgit Richter"
  ],
  "comment": "Minor changes, section on Frobenius algebra structure removed. Final version: to appear in Central European Journal of Mathematics under title `Galois theory and Lubin-Tate cochains on classifying spaces'",
  "categories": [
    "math.AT",
    "math.RA"
  ],
  "abstract": "We consider brave new cochain extensions $F(BG_+,R)\\to F(EG_+,R)$, where $R$ is either a Lubin-Tate spectrum $E_n$ or the related 2-periodic Morava K-theory $K_n$, and $G$ is a finite group. When $R$ is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a $G$-Galois extension in the sense of John Rognes, but not always faithful. We prove that for $E_n$ and $K_n$ these extensions are always faithful in the $K_n$ local category. However, for a cyclic $p$-group $C_{p^r}$, the cochain extension $F({BC_{p^r}}_+,E_n) \\to F({EC_{p^r}}_+,E_n)$ is not a Galois extensions because it ramifies. As a consequence, it follows that the $E_n$-theory Eilenberg-Moore spectral sequence for $G$ and $BG$ does not always converge to its expected target.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-05-31T08:45:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P43",
      "13B05",
      "55N22",
      "55P60"
    ],
    "keywords": [
      "finite group",
      "lubin-tate cohomology",
      "classifying spaces",
      "galois extension",
      "cochain extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1662B"
    }
  }
}