{
  "abstract": "In this paper, we prove that for a smooth complete intersection $X\\subset \\mathbb{P}^n$ of type $(d_1,\\dots,d_c)$ over a number field $k$, there exists an effective bound $N_{\\mathrm{AP}}(d_1,\\dots,d_c)$ such that if $n\\ge N_{\\mathrm{AP}}(d_1,\\dots,d_c)$, then $X$ satisfies arithmetic purity of strong approximation. We establish a connecting lemma that promotes weak approximation to strong approximation under a suitable connectivity hypothesis via rational curves over $k$. We construct the required connecting conics by combining the deformation theory of rational curves with results from the circle method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27027",
  "author_total": 1,
  "authors": [
    {
      "name": "Chen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/080esyrnaxay6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27027",
  "fulltext_url": null,
  "id": "080esyrnaxay6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27027",
  "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": "W7204535078",
  "pdf_url": "https://arxiv.org/pdf/2608.27027",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/080esyrnaxay6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2608.27027",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27027"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Arithmetic purity of strong approximation for complete intersections of large dimension",
  "title_text": "Arithmetic purity of strong approximation for complete intersections of large dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/080esyrnaxay6",
  "venue": "arXiv",
  "versions": []
}