{
  "id": "1807.10862",
  "version": "v1",
  "published": "2018-07-28T01:11:20.000Z",
  "updated": "2018-07-28T01:11:20.000Z",
  "title": "Simple $\\mathcal{L}$-invariants for $\\mathrm{GL}_n$",
  "authors": [
    "Yiwen Ding"
  ],
  "comment": "55 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $L$ be a finite extension of $\\mathbb{Q}_p$, and $\\rho_L$ be an $n$-dimensional semi-stable non crystalline $p$-adic representation of $\\mathrm{Gal}_L$ with full monodromy rank. Via a study of Breuil's (simple) $\\mathcal{L}$-invariants, we attach to $\\rho_L$ a locally $\\mathbb{Q}_p$-analytic representation $\\Pi(\\rho_L)$ of $\\mathrm{GL}_n(L)$, which carries the exact information of the Fontaine-Mazur simple $\\mathcal{L}$-invariants of $\\rho_L$. When $\\rho_L$ comes from an automorphic representation of $G(\\mathbb{A}_{F^+})$ (for a unitary group $G$ over a totally real filed $F^+$ which is compact at infinite places and $\\mathrm{GL}_n$ at $p$-adic places), we prove under mild hypothesis that $\\Pi(\\rho_L)$ is a subrerpresentation of the associated Hecke-isotypic subspaces of the Banach spaces of $p$-adic automorphic forms on $G(\\mathbb{A}_{F^+})$. In other words, we prove the equality of Breuil's simple $\\mathcal{L}$-invariants and Fontaine-Mazur simple $\\mathcal{L}$-invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-28T01:11:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariants",
      "fontaine-mazur simple",
      "dimensional semi-stable non crystalline",
      "adic automorphic forms",
      "full monodromy rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}