{
  "abstract": "If $G$ is a connected reductive algebraic group over a field $k$ of characteristic $\\ell$, we show that both the Lie-theoretic and group-theoretic commuting schemes associated to $G$ are normal and Cohen--Macaulay when $\\ell = 0$, or $\\ell$ is larger than the Coxeter numbers of all simple factors of $G$, and that $\\ell \\neq 19$ (resp. $\\ell \\neq 31$) when $G$ has a simple factor of type $E_7$ (resp. $E_8$). The main new ingredients are provided by studying the unipotent categorical Langlands functor of Zhu. Along the way we prove a $t$-exactness result for a finite unipotent categorical Langlands functor which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27360",
  "author_total": 2,
  "authors": [
    {
      "name": "Jack Sempliner"
    },
    {
      "name": "Xiangqian Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5enn4khrqe7jt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27360",
  "fulltext_url": null,
  "id": "5enn4khrqe7jt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27360",
  "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.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214236915",
  "pdf_url": "https://arxiv.org/pdf/2609.27360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5enn4khrqe7jt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27360"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the normality of the commuting scheme",
  "title_text": "On the normality of the commuting scheme",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5enn4khrqe7jt",
  "venue": "arXiv",
  "versions": []
}