{
  "abstract": "Let $\\mathbf{f}$ be a Hida family of cusp forms over a standard (power series) Iwasawa algebra. We determine the pseudo-isomorphism class of the big Shafarevich-Tate group attached to $\\mathbf{f}$ over a suitable imaginary quadratic field by describing all its higher Fitting ideals; this description is given in terms of the universal Kolyvagin system of Howard's big Heegner points. As a second contribution, we study the variation of the structure of the Shafarevich-Tate groups of the classical specializations of $\\mathbf{f}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22226",
  "author_total": 4,
  "authors": [
    {
      "name": "Enrico Da Ronche"
    },
    {
      "name": "Matteo Longo"
    },
    {
      "name": "Stefano Vigni"
    },
    {
      "name": "Francesco Zerman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ppjtebp06ndc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22226",
  "fulltext_url": null,
  "id": "5ppjtebp06ndc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22226",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7222403678",
  "pdf_url": "https://arxiv.org/pdf/2610.22226",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ppjtebp06ndc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22226",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22226"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Variation of Shafarevich-Tate groups in Hida families",
  "title_text": "Variation of Shafarevich-Tate groups in Hida families",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/5ppjtebp06ndc",
  "venue": "arXiv",
  "versions": []
}