{
  "id": "2501.13580",
  "version": "v1",
  "published": "2025-01-23T11:39:19.000Z",
  "updated": "2025-01-23T11:39:19.000Z",
  "title": "Multivariable $(\\varphi_q,\\mathcal{O}_K^{\\times})$-modules associated to $p$-adic representations of $\\mathrm{Gal}(\\overline{K}/K)$",
  "authors": [
    "Changjiang Du"
  ],
  "comment": "48 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be an unramified extension of $\\mathbb{Q}_p$, and $E$ a finite extension of $K$ with ring of integers $\\mathcal{O}_E$. We associate to every finite type continuous $\\mathcal{O}_E$-representation $\\rho$ of $\\mathrm{Gal}(\\overline{K}/K)$ an \\'etale $(\\varphi_q,\\mathcal{O}_K^{\\times})$-module $D_{A_{\\mathrm{mv},E}}^{(0)}(\\rho)$ over $A_{\\mathrm{mv},E}$, where $A_{\\mathrm{mv},E}$ is the $p$-adic completion of a completed localization of the Iwasawa algebra $\\mathcal{O}_E[\\negthinspace[\\mathcal{O}_K]\\negthinspace]$. Furthermore, we prove that the functor $D_{A_{\\mathrm{mv},E}}^{(0)}$ is fully faithful and exact. This functor is a $p$-adic analogue of $D_A^{(0)}$ in the recent work of Breuil, Herzig, Hu, Morra and Schraen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-23T11:39:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic representations",
      "finite extension",
      "multivariable",
      "adic completion",
      "iwasawa algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}