{
  "id": "1705.02638",
  "version": "v1",
  "published": "2017-05-07T15:47:17.000Z",
  "updated": "2017-05-07T15:47:17.000Z",
  "title": "On the exactness of ordinary parts over a local field of characteristic $p$",
  "authors": [
    "Julien Hauseux"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected reductive group over a non-archimedean local field $F$ of characteristic $p$, $P$ be a parabolic subgroup of $G$, and $R$ be an artinian ring in which $p$ is nilpotent. We prove that the ordinary part functor $\\mathrm{Ord}_P$ is exact on the category of admissible smooth $R$-representations of $G$. We derive some consequences about extensions between admissible smooth $R$-representations of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-07T15:47:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "characteristic",
      "non-archimedean local field",
      "ordinary part functor",
      "admissible smooth",
      "parabolic subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}