{
  "id": "1307.1356",
  "version": "v1",
  "published": "2013-07-04T14:43:12.000Z",
  "updated": "2013-07-04T14:43:12.000Z",
  "title": "On equivariant Euler-Poincaré characteristic in sheaf cohomology",
  "authors": [
    "Steffen Kionke",
    "Jürgen Rohlfs"
  ],
  "comment": "7 pages, no figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let X be a topological Hausdorff space together with a continuous action of a finite group G. Let R be the ring of integers of a number field F. Let E be a G-sheaf of flat R-modules over X and let $\\Phi$ be a G-stable paracompactifying family of supports on X. We show that under some natural cohomological finiteness conditions the Lefschetz number of the action of g in G on the cohomology $H_\\Phi(X,E) \\otimes_{R} F$ equals the Lefschetz number of the g-action on $H_\\Phi(X^g, E_{|X^g}) \\otimes_{R} F$, where $X^g$ is the set of fixed points of g in X. More generally, the class $\\sum_j (-1)^j [H^j_\\Phi (X,E) \\otimes_R F]$ in the character group equals a sum of representations induced from irreducible F-rational representations $V_\\lambda$ of $H$ where $H$ runs in the set of G-conjugacy classes of subgroups of G. The integral coefficients $m_\\lambda$ in this sum are explicitly determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-04T14:43:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N30",
      "54H15"
    ],
    "keywords": [
      "sheaf cohomology",
      "characteristic",
      "equivariant",
      "lefschetz number",
      "natural cohomological finiteness conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1356K"
    }
  }
}