{
  "abstract": "We prove that generically on the basic stratum of split unitary Shimura varieties, the universal abelian variety with endomorphism structure and polarization has minimal automorphism group in a precise sense, except for a few degenerate cases. This is a direct analogue of Oort's conjecture on automorphisms of supersingular abelian varieties. On the way, we explicitly compute the generic automorphism group of the universal $p$-divisible group in a given basic isogeny class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04072",
  "author_total": 3,
  "authors": [
    {
      "name": "Paul Philippe"
    },
    {
      "name": "Fabian Schnelle"
    },
    {
      "name": "Eva Viehmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1yxkkm68q7qnt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04072",
  "fulltext_url": null,
  "id": "1yxkkm68q7qnt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04072",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7208783885",
  "pdf_url": "https://arxiv.org/pdf/2609.04072",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1yxkkm68q7qnt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.04072",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04072"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Oort's conjecture for split unitary Shimura varieties",
  "title_text": "Oort's conjecture for split unitary Shimura varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/1yxkkm68q7qnt",
  "venue": "arXiv",
  "versions": []
}