{
  "abstract": "Let $G$ be a simple abelian variety of dimension $g \\in \\mathbb{N}$ defined over $\\mathbb{Q}^\\mathrm{alg}$ and let $C_1, C_2 \\subseteq G^N(\\mathbb{C})$ be irreducible closed algebraic curves with $N \\geq 3$. Further assume that at least one of $C_1$ and $C_2$ is not defined over $\\mathbb{Q}^\\mathrm{alg}$. Suppose that there does not exist an algebraic subgroup $H_1 \\subseteq G^N(\\mathbb{C})$ of dimension $g$ such that $C_1 \\subseteq H_1$ and that there does not exist an algebraic subgroup $H_2 \\subseteq G^N(\\mathbb{C})$ of dimension $2g$ such that $C_1 \\cup C_2 \\subseteq H_2$. Denoting $\\mathcal{N} = \\{n \\in \\mathbb{N} \\ | \\ [n]C_1 \\subseteq C_2\\}$, we prove that $\\bigcup_{n \\in \\mathbb{N} \\setminus \\mathcal{N}}\\{x \\in C_1 \\ | \\ nx \\in C_2\\}$ is finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10209",
  "author_total": 1,
  "authors": [
    {
      "name": "David J. Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7j3qd6h8p4a6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10209",
  "fulltext_url": null,
  "id": "7j3qd6h8p4a6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10209",
  "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.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220971515",
  "pdf_url": "https://arxiv.org/pdf/2610.10209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7j3qd6h8p4a6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Points and their multiples on curves in powers of simple abelian varieties",
  "title_text": "Points and their multiples on curves in powers of simple abelian varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/7j3qd6h8p4a6x",
  "venue": "arXiv",
  "versions": []
}