{
  "abstract": "In this paper, we study supersingularity of modular Jacobians $J_0(N)$ and abelian varieties $A_f$ of $\\mathrm{GL}_{2}$-type from both the vertical perspective (where the prime $p$ is fixed, and the level $N$ varies) and the horizontal perspective (where the newform $f$ is fixed, and the prime $p$ varies). Vertically, we prove that $J_{0}(N)$ is supersingular modulo a given prime $p$ for only finitely many levels $N$. Horizontally, we show that for sufficiently large $p$, the reduction of $A_f$ modulo $p$ is supersingular if and only if it isogenous to a power of a supersingular elliptic curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17819",
  "author_total": 4,
  "authors": [
    {
      "name": "Aarya J. Kumar"
    },
    {
      "name": "Sargam Mondal"
    },
    {
      "name": "Erick Ross"
    },
    {
      "name": "Hui Xue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9yfp7rkj47ra.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17819",
  "fulltext_url": null,
  "id": "e9yfp7rkj47ra",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17819",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213510001",
  "pdf_url": "https://arxiv.org/pdf/2609.17819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9yfp7rkj47ra.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Only finitely many modular Jacobians are supersingular modulo a given prime",
  "title_text": "Only finitely many modular Jacobians are supersingular modulo a given prime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/e9yfp7rkj47ra",
  "venue": "arXiv",
  "versions": []
}