{
  "id": "2011.09163",
  "version": "v1",
  "published": "2020-11-18T09:14:12.000Z",
  "updated": "2020-11-18T09:14:12.000Z",
  "title": "$(G,μ)$-Windows and Deformations of $(G,μ)$-Displays",
  "authors": [
    "Oliver Bueltel",
    "Mohammad Hadi Hedayatzadeh"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $k_0$ be a finite field of characteristic $p$, let $G$ be a smooth affine group scheme over $\\mathbb{Z}_p$, and let $\\mu$ be a cocharacter of $G_{W(k_0)}$ such that the set of $\\mu$-weights of $\\text{Lie}\\, G$ is a subset of $\\{-1,0,1,2,\\dots\\}$. We prove that the groupoid of adjoint nilpotent $(G,\\mu)$-displays is equivalent to the groupoid of $(G,\\mu)$-windows, which are the generalizations of windows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-18T09:14:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformations",
      "smooth affine group scheme",
      "finite field",
      "adjoint nilpotent",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}