{
  "abstract": "Let $K/\\Qp$ be a finite extension, $\\bG$ a connected reductive group over $K$, and set $G = \\bG(K)$, considered as a $p$-adic Lie group. We show first that the Bernstein center $\\cC_G$ of the category of solid locally $\\Qp$-analytic representations of $G$ is isomorphic to the center of the locally analytic distribution algebra $D^\\la(G)$. We then consider the Emerton-Gee stack $\\frX_{n,K}$ of rank-$n$ $(\\vphi,Γ)$-modules over the Robba ring for $K$ and determine its connected components. The latter are in canonical bijection with the primitive idempotents of the ring $\\cC_{\\GL_n(K)}$. Moreover, under the assumption that the ring of global functions on $\\frX_{n,K}$ has no non-zero locally nilpotent elements, we show that this ring is isomorphic to a Fréchet completion of $\\cC_{\\GL_n(K)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07648",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel Le"
    },
    {
      "name": "Matthias Strauch"
    },
    {
      "name": "Zichuan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e2b202xj4nbcw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07648",
  "fulltext_url": null,
  "id": "e2b202xj4nbcw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07648",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221054074",
  "pdf_url": "https://arxiv.org/pdf/2610.07648",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e2b202xj4nbcw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.07648",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07648"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Block decompositions in the p-adic Langlands correspondence",
  "title_text": "Block decompositions in the p-adic Langlands correspondence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/e2b202xj4nbcw",
  "venue": "arXiv",
  "versions": []
}