{
  "abstract": "Let $F$ be a finite extension of $\\mathbb Q_p$ and $p\\geq 5$. In this paper, we establish homological branching laws for mod $p$ representations of $\\mathrm{GL}_2(F)$ restricted to split and nonsplit maximal tori, treating principal and special series and, when $F=\\mathbb Q_p$, supersingular representations. We determine the derived Hom-complexes in both orders for nonexceptional characters. At exceptional characters, we calculate their Euler--Poincaré characteristics under a $p$-torsion-freeness hypothesis. We also establish corresponding results for a class of unitary Banach space representations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29629",
  "author_total": 2,
  "authors": [
    {
      "name": "Yang Chen"
    },
    {
      "name": "Haoran Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b834rvemfcav8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29629",
  "fulltext_url": null,
  "id": "b834rvemfcav8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29629",
  "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": "W7223236112",
  "pdf_url": "https://arxiv.org/pdf/2610.29629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b834rvemfcav8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Homological branching laws for $p$-adic and mod $p$ representations of ${\\rm GL}_2$ over a $p$-adic field",
  "title_text": "Homological branching laws for p-adic and mod p representations of GL_2 over a p-adic field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/b834rvemfcav8",
  "venue": "arXiv",
  "versions": []
}