{
  "abstract": "We prove a $p$-adic divisibility between the automorphic periods of a cuspidal automorphic representation $π$ of $\\mathrm{GL}_3(\\mathbb{Q})$ and the periods of its Arthur-Clozel base change to a real quadratic field $E$. As a corollary, we establish a divisibility predicted by the Bloch-Kato conjecture for the adjoint motive of $π$ twisted by an even quadratic character. This generalizes earlier works of Tilouine-Urban and Hida in the case of classical modular forms. The divisibility we prove involves a new kind of automorphic periods for conjugate self-dual cuspidal automorphic representations of $\\mathrm{GL}_3(E)$, defined within the middle degree of the cuspidal cohomology instead of the top or bottom degrees. Moreover, we prove an à la Hida adjoint $L$-value formula for $\\mathrm{GL}_3(E)$ that relates these newly defined middle-degree periods to the usual top and bottom automorphic periods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26477",
  "author_total": 1,
  "authors": [
    {
      "name": "Tristan Ricoul"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nnh48n68sbgk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26477",
  "fulltext_url": null,
  "id": "3nnh48n68sbgk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26477",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214068676",
  "pdf_url": "https://arxiv.org/pdf/2609.26477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nnh48n68sbgk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A divisibility of automorphic periods for the real quadratic base change of $\\mathrm{GL}_3$",
  "title_text": "A divisibility of automorphic periods for the real quadratic base change of GL_3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/3nnh48n68sbgk",
  "venue": "arXiv",
  "versions": []
}