{
  "abstract": "We construct a new type of congruence from irregular weight mod $p$ Picard modular forms (for $p$ inert) to ones of regular weight, analogous to the one obtained by Kansal--Levin--Savitt in the Hilbert setting. The congruence is obtained by using a geometric Jacquet--Langlands phenomenon, as first established by Vollaard, to transfer irregular weight mod $p$ Picard modular forms from the Picard modular surface to a Shimura set. We call this an exotic congruence, since it relates mod $p$ automorphic forms associated to different groups. This congruence will be used in upcoming work of the author proving mod $p$ local-global compatibility for irregular weight Picard modular forms (in the $p$ inert case).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26807",
  "author_total": 1,
  "authors": [
    {
      "name": "Calle Sönne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apmsrc33br3da.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26807",
  "fulltext_url": null,
  "id": "apmsrc33br3da",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26807",
  "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"
    ],
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      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223055750",
  "pdf_url": "https://arxiv.org/pdf/2610.26807",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apmsrc33br3da.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26807",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26807"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An Exotic Congruence for Irregular Weight Picard Modular Forms",
  "title_text": "An Exotic Congruence for Irregular Weight Picard Modular Forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/apmsrc33br3da",
  "venue": "arXiv",
  "versions": []
}