{
  "abstract": "We show that any $d$-dimensional local ring $A$ with a dualizing complex, $\\mathrm{depth} A=d-1$, and cyclic deficiency module $K^{d-1}(A)$ admits a maximal Cohen--Macaulay module. It is constructed as the unique nonzero cohomology module of the cone of the derived morphism induced by a surjection $A\\to K^{d-1}(A)$. This gives new cases of the small Cohen--Macaulay conjecture. When $A$ is quasi-Gorenstein, this module is identified with the first syzygy of the canonical module $ω_{A/xA}$, for any $x\\in\\operatorname{ann}_A K^{d-1}(A)$ that is regular on $A$. This recovers a theorem of Tavanfar and Shimomoto for quasi-Gorenstein deformations of a 3-dimensional quasi-Gorenstein local ring $A$ with $K^2(A)\\cong k$. We also construct examples of section rings satisfying the hypotheses of our theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.10962",
  "author_total": 1,
  "authors": [
    {
      "name": "Likun Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22v19nk5nefp3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.10962",
  "fulltext_url": null,
  "id": "22v19nk5nefp3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.10962",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7202244344",
  "pdf_url": "https://arxiv.org/pdf/2608.10962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22v19nk5nefp3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2608.10962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.10962"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On an Instance of the Small Cohen-Macaulay Conjecture II",
  "title_text": "On an Instance of the Small Cohen-Macaulay Conjecture II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/22v19nk5nefp3",
  "venue": "arXiv",
  "versions": []
}