{
  "id": "2501.03644",
  "version": "v1",
  "published": "2025-01-07T09:22:37.000Z",
  "updated": "2025-01-07T09:22:37.000Z",
  "title": "Finite length for unramified $\\mathrm{GL}_2$",
  "authors": [
    "Christophe Breuil",
    "Florian Herzig",
    "Yongquan Hu",
    "Stefano Morra",
    "Benjamin Schraen"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $p$ be a prime number and $K$ a finite unramified extension of $\\mathbb{Q}_p$. If $p$ is large enough with respect to $[K:\\mathbb{Q}_p]$ and under mild genericity assumptions, we prove that the admissible smooth representations of $\\mathrm{GL}_2(K)$ that occur in Hecke eigenspaces of the mod $p$ cohomology are of finite length. We also prove many new structural results about these representations of $\\mathrm{GL}_2(K)$ and their subquotients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-07T09:22:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite length",
      "mild genericity assumptions",
      "structural results",
      "prime number",
      "finite unramified extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}