{
  "abstract": "Bhatt-Morrow-Scholze motivic filtration on topological Hochschild homology ($THH$) is extended to Azumaya algebras over quasisyntomic rings. We prove the Azumaya descent theorem: $THH$ of such an algebra is equivalent, as an underlying spectrum, to $THH$ of its center, normalized on $π_0$ by the reduced trace instead of the unit map. This comparison $Φ_A$ is not shown to be étale-locally cyclotomic. But what is cyclotomic étale-locally is a separate Morita trace, agreeing with $Φ_A$ only on $π_0$. The resulting transported filtration is exactly the center BMS filtration, well defined up to the automorphism ambiguity of $Φ_A$. It is insensitive to the Brauer class, reflected instead by $K$-theoretic and module-categorical pairings $THH$ does not see. We establish the analogous statement for derived Azumaya algebras over connective $\\mathbb{E}_\\infty$-rings, under a connectivity hypothesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02870",
  "author_total": 2,
  "authors": [
    {
      "name": "Hông Vân Lê"
    },
    {
      "name": "Alexander Zuevsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7rjpvb54vcyd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02870",
  "fulltext_url": null,
  "id": "b7rjpvb54vcyd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02870",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7220432813",
  "pdf_url": "https://arxiv.org/pdf/2610.02870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7rjpvb54vcyd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.02870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Azumaya descent and étale-local cyclotomic comparison: a noncommutative filtration",
  "title_text": "Azumaya descent and étale-local cyclotomic comparison: a noncommutative filtration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/b7rjpvb54vcyd",
  "venue": "arXiv",
  "versions": []
}