{
  "id": "2009.09044",
  "version": "v1",
  "published": "2020-09-18T19:52:23.000Z",
  "updated": "2020-09-18T19:52:23.000Z",
  "title": "$G$-displays of Hodge type and formal $p$-divisible groups",
  "authors": [
    "Patrick Daniels"
  ],
  "comment": "45 pages, comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $G$ be a smooth group scheme over the $p$-adic integers with reductive generic fiber, and let $\\mu$ be a minuscule cocharacter for $G$ which remains minuscule in a faithful representation of $G$. We show that the category of nilpotent $(G,\\mu)$-displays over $p$-nilpotent rings $R$ embeds fully faithfully into the category of formal $p$-divisible groups over $R$ equipped with crystalline Tate tensors, and that the embedding becomes an equivalence when $R/pR$ has a $p$-basis \\'etale locally. The definition of the embedding relies on the construction of a G-crystal (i.e., an exact tensor functor from representations of G to crystals in finite locally free $\\mathcal{O}_{\\text{Spec } R/ \\mathbb{Z}_p}$-modules) associated to any adjoint nilpotent $(G,\\mu)$-display, which extends the construction of the crystal associated to a nilpotent Zink display. As applications, we obtain an explicit comparison between the Rapoport-Zink functors of Hodge type defined by Kim and by B\\\"ueltel and Pappas, and we extend a theorem of Faltings regarding deformations of connected $p$-divisible groups with crystalline Tate tensors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-18T19:52:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divisible groups",
      "hodge type",
      "crystalline tate tensors",
      "nilpotent zink display",
      "smooth group scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}