{
  "abstract": "Let $A=Q/(\\mathbf f)$, where $Q$ is a polynomial ring over an infinite field $k$ and $\\mathbf f=f_1,\\ldots,f_c$ is a homogeneous $Q$-regular sequence. For $1\\leq j\\leq c$, set $w_j=\\operatorname{deg}(f_j)>0.$ Let $M$ be a finitely generated graded $A$-module of infinite projective dimension. Set $M_i=\\operatorname{Syz}_i^A(M)$. We prove that, for each $l\\in\\{0,1\\}$, the sets $\\operatorname{Ass}_A(M_{2i+l})$ eventually stabilize, and that $\\operatorname{reg}(M_{2i+l})$ is eventually bounded above and below by linear polynomials. If $w_j=w$ for all $1\\leq j\\leq c$, then the functions $i\\longmapsto \\operatorname{reg}(M_{2i+l})$, $i\\longmapsto v(M_{2i+l}),$ and $i\\longmapsto v_{\\mathfrak p}(M_{2i+l}),\\, \\mathfrak p\\in\\mathcal A_l,$ are eventually linear with leading coefficient $w$, where $\\mathcal A_l$ denotes the stable set of associated primes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29855",
  "author_total": 1,
  "authors": [
    {
      "name": "Samarendra Sahoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91ekrfr765hqg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29855",
  "fulltext_url": null,
  "id": "91ekrfr765hqg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29855",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7223250563",
  "pdf_url": "https://arxiv.org/pdf/2610.29855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91ekrfr765hqg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Regularity and $v$-number of syzygies of graded maximal Cohen-Macaulay modules",
  "title_text": "Regularity and v-number of syzygies of graded maximal Cohen-Macaulay modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/91ekrfr765hqg",
  "venue": "arXiv",
  "versions": []
}