{
  "id": "1106.4354",
  "version": "v1",
  "published": "2011-06-22T00:41:33.000Z",
  "updated": "2011-06-22T00:41:33.000Z",
  "title": "Generalized support varieties for finite group schemes",
  "authors": [
    "Eric M. Friedlander",
    "Julia Pevtsova"
  ],
  "journal": "Documenta Mathematica, Extra Volume Suslin (2011) 191-217",
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct two families of refinements of the (projectivized) support variety of a finite dimensional module $M$ for a finite group scheme $G$. For an arbitrary finite group scheme, we associate a family of {\\it non maximal rank varieties} $\\Gamma^j(G)_M$, $1\\leq j \\leq p-1$, to a $kG$-module $M$. For $G$ infinitesimal, we construct a finer family of locally closed subvarieties $V^{\\ul a}(G)_M$ of the variety of one parameter subgroups of $G$ for any partition $\\ul a$ of $\\dim M$. For an arbitrary finite group scheme $G$, a $kG$-module $M$ of constant rank, and a cohomology class $\\zeta$ in $\\HHH^1(G,M)$ we introduce the {\\it zero locus} $Z(\\zeta) \\subset \\Pi(G)$. We show that $Z(\\zeta)$ is a closed subvariety, and relate it to the non-maximal rank varieties. We also extend the construction of $Z(\\zeta)$ to an arbitrary extension class $\\zeta \\in \\Ext^n_G(M,N)$ whenever $M$ and $N$ are $kG$-modules of constant Jordan type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-22T00:41:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "20C20",
      "20G10"
    ],
    "keywords": [
      "generalized support varieties",
      "support variety",
      "arbitrary finite group scheme",
      "non maximal rank varieties",
      "arbitrary extension class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4354F"
    }
  }
}