{
  "abstract": "Let $R = S/(f)$ be a complete local hypersurface ring and let $A = S[\\![u,v]\\!]/(f+uv)$. Pfister and Popescu showed that the stable categories of maximal Cohen-Macaulay modules over $R$ and over $A$ are equivalent, with no assumption on the characteristic. We give a short proof. If $(Φ,Ψ)$ is a matrix factorization of $h$ and $\\partial$ is a derivation, then $(\\partialΨ,\\partialΦ)$ is a null-homotopy for multiplication by $\\partial h$. Since $u$ and $v$ are partial derivatives of $f+uv$, they act as zero on the stable category of $A$, so the Koszul complex on $u$ and $v$ splits in the singularity category, and this gives density. For the double branched cover $S[\\![z]\\!]/(f+z^2)$ the same argument yields $2z$: it recovers Knörrer's lemma up to free summands on the double branched cover when $2$ is a unit, and we show by an example that this lemma, and periodicity for the iterated double branched cover $S[\\![z,w]\\!]/(f+z^2+w^2)$, fail in characteristic two. We also compute the second syzygy over $A$ of a maximal Cohen-Macaulay $R$-module by an explicit resolution, and show that the change of basis used there cannot be given by a universal matrix formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37839",
  "author_total": 1,
  "authors": [
    {
      "name": "Graham J. Leuschke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4c8tjv1y803dg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37839",
  "fulltext_url": null,
  "id": "4c8tjv1y803dg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37839",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214996850",
  "pdf_url": "https://arxiv.org/pdf/2609.37839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4c8tjv1y803dg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.37839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37839"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A new proof of characteristic-free Knörrer periodicity",
  "title_text": "A new proof of characteristic-free Knörrer periodicity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4c8tjv1y803dg",
  "venue": "arXiv",
  "versions": []
}