{
  "id": "2306.09696",
  "version": "v1",
  "published": "2023-06-16T09:00:54.000Z",
  "updated": "2023-06-16T09:00:54.000Z",
  "title": "The canonical dimension of modules for Iwasawa algebras",
  "authors": [
    "James Timmins"
  ],
  "comment": "37 pages",
  "categories": [
    "math.NT",
    "math.RA",
    "math.RT"
  ],
  "abstract": "Let F be a non-trivial finite extension of the p-adic numbers, and G be a compact p-adic Lie group whose Lie algebra is isomorphic to a split simple F-Lie algebra. We prove that the mod p Iwasawa algebra of G has no modules of canonical dimension one. One consequence is a new upper bound on the Krull dimension of the Iwasawa algebra. We also prove a canonical dimension-theoretic criterion for a mod p smooth admissible representation to be of finite length. Combining our results shows that any smooth admissible representation of $GL_n(F)$, with central character, has finite length if its dual has canonical dimension two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-16T09:00:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16P60",
      "16P90",
      "22E50"
    ],
    "keywords": [
      "iwasawa algebra",
      "canonical dimension",
      "smooth admissible representation",
      "finite length",
      "compact p-adic lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}