{
  "abstract": "We prove Kato's main conjecture for modular forms at nonordinary primes for weights in the Fontaine-Laffaille range. The key ingredients in the proof are a reformulation of the conjecture in terms of signed Selmer groups due to Lei-Loeffler-Zerbes, certain $p$-adic families of Rankin-Eisenstein classes arising from the work of Lei-Loeffler-Zerbes and Kings-Loeffler-Zerbes, and the lower bound divisibility in an Iwasawa-Greenberg main conjecture for Rankin-Selberg $p$-adic $L$-functions obtained in our earlier work \\cite{CLW}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29470",
  "author_total": 3,
  "authors": [
    {
      "name": "Francesc Castella"
    },
    {
      "name": "Zheng Liu"
    },
    {
      "name": "Xin Wan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f17d8erxv8w4y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29470",
  "fulltext_url": null,
  "id": "f17d8erxv8w4y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29470",
  "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"
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  ],
  "openalex": "W7204929867",
  "pdf_url": "https://arxiv.org/pdf/2608.29470",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f17d8erxv8w4y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29470",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29470"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Kato's main conjecture for nonordinary modular forms",
  "title_text": "Kato's main conjecture for nonordinary modular forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/f17d8erxv8w4y",
  "venue": "arXiv",
  "versions": []
}