{
  "id": "2311.03740",
  "version": "v1",
  "published": "2023-11-07T05:50:55.000Z",
  "updated": "2023-11-07T05:50:55.000Z",
  "title": "Reductions of semi-stable representations using the Iwahori mod $p$ Local Langlands Correspondence",
  "authors": [
    "Anand Chitrao",
    "Eknath Ghate"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We determine the mod $p$ reductions of all two-dimensional semi-stable representations $V_{k,\\mathcal{L}}$ of the Galois group of $\\mathbb{Q}_p$ of weights $3 \\leq k \\leq p+1$ and $\\mathcal{L}$-invariants $\\mathcal{L}$ for primes $p \\geq 5$. In particular, we describe the constants appearing in the unramified characters completely. The proof involves computing the reduction of Breuil's $\\mathrm{GL}_2(\\mathbb{Q}_p)$-Banach space $\\tilde{B}(k,\\mathcal{L})$, by studying certain logarithmic functions using background material developed by Colmez, and then applying an Iwahori theoretic version of the mod $p$ Local Langlands Correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-07T05:50:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80"
    ],
    "keywords": [
      "local langlands correspondence",
      "iwahori mod",
      "iwahori theoretic version",
      "galois group",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}