{
  "abstract": "We prove that for a very general abelian variety of dimension $\\geq 4$, a divisor $D\\in {\\rm CH}^1(A)$ that satisfies $D^2=0$ in ${\\rm CH}^2(A)$ is of torsion. The same result is also established for a very general Jacobian in genus $4$. We use then the second statement in order to prove a conjecture of Pirola, which states that any rational section of the Kummer fibration $K=J/\\pm {\\rm Id}\\rightarrow \\mathcal{M}_4$, where $J\\rightarrow \\mathcal{M}_4 $ is the Jacobian fibration, must be a multiple of the Griffiths-Pirola section given by the difference of the two trigonal divisors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.07053",
  "author_total": 1,
  "authors": [
    {
      "name": "Claire Voisin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7d78d088w1ca1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.07053",
  "fulltext_url": null,
  "id": "7d78d088w1ca1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.07053",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7167811593",
  "pdf_url": "https://arxiv.org/pdf/2607.07053",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7d78d088w1ca1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2607.07053",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.07053"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Chow ring of very general abelian varieties and a question of Pirola",
  "title_text": "On the Chow ring of very general abelian varieties and a question of Pirola",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/7d78d088w1ca1",
  "venue": "arXiv",
  "versions": []
}