{
  "abstract": "We prove Z-stability for all simple, separable, pure, nuclear C*-algebras. Combining this with very recent work of Thiel completes the proof of the Toms-Winter conjecture. We do this through the framework of II_1 factorial tracially complete C*-algebras. We characterise regularity for these algebras in various terms. In particular they are regular if and only if they have real rank zero and the Murray-von Neumann equivalence classes of projections correspond to continuous affine functions from the designated traces to [0,1]. As an application of our analysis of ultrapowers of tracial completions, we show simple pure C*-algebras whose quasitraces are traces are K-stable. In the amenable setting we give a local quantisation result, a la Popa, for II_1 factorial amenable tracially complete C*-algebras, which obtains hyperfiniteness from regularity conditions. Our Z-stability results follow from this together with a theorem of Matui and Sato. An initial version of an essential lemma in the Bauer trace simplex case was obtained from ChatGPT Astra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09390",
  "author_total": 6,
  "authors": [
    {
      "name": "Samuel Evington"
    },
    {
      "name": "Shanshan Hua"
    },
    {
      "name": "Christopher Schafhauser"
    },
    {
      "name": "Apurva Seth"
    },
    {
      "name": "Aaron Tikuisis"
    },
    {
      "name": "Stuart White"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37c14k99qj12n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09390",
  "fulltext_url": null,
  "id": "37c14k99qj12n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09390",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7220918640",
  "pdf_url": "https://arxiv.org/pdf/2610.09390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37c14k99qj12n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regular simple nuclear C*-algebras",
  "title_text": "Regular simple nuclear C*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/37c14k99qj12n",
  "venue": "arXiv",
  "versions": []
}