{
  "abstract": "Let $K$ be a number field containing a primitive $p$-th root of unity $ζ_p$. Let $f(x)\\in K[x]$ be a monic integral polynomial, and let $f_0$ denote its radical. Let $C/K$ be the superelliptic curve defined by $y^p=f(x)$, and let $J$ be its Jacobian variety. The variety $J$ admits multiplication by $ζ_p$ over $K$; in particular, the endomorphism induced by $Π:=1-ζ_p$ gives an isogeny of $J$ over $K$. Let $\\operatorname{Sel}_Π(J)$ denote the Selmer group associated to $Π$. Under suitable hypotheses, we obtain bounds for $\\operatorname{Sel}_Π(J)$ in terms of the $p$-torsion subgroup of the class group of $L:=K[x]/(f_0)$. Several examples illustrating the results are also discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02173",
  "author_total": 1,
  "authors": [
    {
      "name": "Pengfei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bs1x9catvp3wh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02173",
  "fulltext_url": null,
  "id": "bs1x9catvp3wh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02173",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7207566148",
  "pdf_url": "https://arxiv.org/pdf/2609.02173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bs1x9catvp3wh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bounding Selmer Groups of Superelliptic Jacobians via Class Groups",
  "title_text": "Bounding Selmer Groups of Superelliptic Jacobians via Class Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/bs1x9catvp3wh",
  "venue": "arXiv",
  "versions": []
}