{
  "abstract": "We classify reductive monoids over arbitrary base schemes by descent from the split classification in arXiv:2607.00322. For a reductive group scheme $G$, we construct its sheaf of based root data, abstract Cartan torus, abstract Weyl group, and a scheme of Weyl cones. The last of these represents the functor of isomorphism classes of rigidified reductive monoids with unit group $G$. As applications, we deduce a criterion for the existence of monoids that are not groups, prove an extension theorem over normal integral bases, and construct the Vinberg monoids without a quasi-split hypothesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05847",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingren Chi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cp6dtd77xv12a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05847",
  "fulltext_url": null,
  "id": "cp6dtd77xv12a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05847",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220713690",
  "pdf_url": "https://arxiv.org/pdf/2610.05847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cp6dtd77xv12a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of reductive monoids",
  "title_text": "Classification of reductive monoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cp6dtd77xv12a",
  "venue": "arXiv",
  "versions": []
}