{
  "abstract": "Let $\\mathrm{F}/\\mathbb{Q}_p$ be a finite extension with $p\\ne 2$, and let $V$ be a quadratic space over $\\mathrm{F}$ of dimension at least two admitting a self-dual lattice. We prove the local arithmetic Siegel-Weil formula for GSpin Rapoport-Zink spaces formulated by Li and Zhang. We use the global-to-local strategy of Mihatsch and Zhang and its application by Luo. Using a generalization of the prismatic realization functor of Imai, Kato, and Youcis, we construct and study derived special cycles on integral models of SO Shimura varieties and their Rapoport-Zink uniformizations. We derive the local intersection formula from the modularity of special cycles on the generic fiber. As a first application, we prove the corresponding semi-global arithmetic Siegel-Weil identity for orthogonal Shimura varieties over a totally real field $F\\ne\\mathbb{Q}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31173",
  "author_total": 1,
  "authors": [
    {
      "name": "Xuanyou Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b9b1dkc7jv8cr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31173",
  "fulltext_url": null,
  "id": "b9b1dkc7jv8cr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31173",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223262889",
  "pdf_url": "https://arxiv.org/pdf/2610.31173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b9b1dkc7jv8cr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the arithmetic Siegel--Weil formula for orthogonal Shimura varieties over a general totally real field",
  "title_text": "On the arithmetic Siegel--Weil formula for orthogonal Shimura varieties over a general totally real field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/b9b1dkc7jv8cr",
  "venue": "arXiv",
  "versions": []
}