{
  "id": "2505.08094",
  "version": "v1",
  "published": "2025-05-12T21:56:41.000Z",
  "updated": "2025-05-12T21:56:41.000Z",
  "title": "Invariants for $\\mathbb G_{(r)}$-modules",
  "authors": [
    "Eric M. Friedlander"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Following earlier work of C. Bendel, J. Petvsova, P. Sobaje, A. Suslin, and the author, we further investigate refined invariants for finite dimensional representations $M$ of infinitesimal group schemes $\\mathbb G$ over a field $k$ of characteristic $p>0$. In particular, we explore invariants of modules for Frobenius kernels $\\mathbb G_{(r)}$ of linear algebraic groups $\\mathbb G$ of exponential type. Such finite group schemes admit a refinement of support theory, including Jordan type functions and constructions of vector bundles for special classes of $\\mathbb G_{(r)}$-modules. We reformulate earlier results for $\\mathbb G_{(r)}$-modules in terms which are both more explicit and more accessible to computation, yet preserve the usual support theory for $\\mathbb G_{(r)}$-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-12T21:56:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "14L17"
    ],
    "keywords": [
      "invariants",
      "finite group schemes admit",
      "reformulate earlier results",
      "jordan type functions",
      "linear algebraic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}