{
  "abstract": "We prove the unpolarized Shafarevich conjecture for hyper-Kähler varieties of a fixed deformation type, unifying earlier results for K3 surfaces and polarized hyper-Kähler varieties. We also study a cohomological variant in which good reduction is replaced by unramifiedness of cohomology; the resulting finiteness statements depend on the faithfulness of the automorphism action on cohomology. For hyper-Kähler varieties of CM type, we prove finiteness of geometric isomorphism classes in a fixed deformation type over number fields of bounded degree, extending a theorem of Orr and Skorobogatov for K3 surfaces. Our main tool is a uniform Kuga-Satake map, whose arithmetic properties are developed along the way.",
  "abstract_shown": true,
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  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Zhiyuan Li"
    },
    {
      "name": "Lie Fu"
    },
    {
      "name": "Teppei Takamatsu"
    },
    {
      "name": "Haitao Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpex7p4cvf9p9.bib",
  "cited_by": 0,
  "doi": "10.14231/ag-2026-018",
  "fulltext_url": null,
  "id": "fpex7p4cvf9p9",
  "issns": [
    "2214-2584",
    "2313-1691"
  ],
  "landing_url": "https://hal.science/hal-05750255v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
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    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W4221166952",
  "pdf_url": "https://hal.science/hal-05750255/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "Foundation Compositio Mathematica",
  "ris": "https://research.draconitic.com/paper/fpex7p4cvf9p9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05750255",
      "source": "hal",
      "url": "https://hal.science/hal-05750255v1"
    }
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Unpolarized Shafarevich conjectures for hyper-Kähler varieties",
  "title_text": "Unpolarized Shafarevich conjectures for hyper-Kähler varieties",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/fpex7p4cvf9p9",
  "venue": "Algebraic Geometry",
  "versions": []
}