{
  "abstract": "Let $R$ be a Noetherian $\\mathbb{N}$-graded ring. Assume that $L$ and $M$ are finitely generated $\\mathbb{Z}$-graded $R$-module, and $I$ a homogeneous ideal of $R$. Let $N$ be a graded submodule of $M$. Fix $k\\in \\mathbb{N}$. Denote $H:=\\operatorname{Ext}^k_R(L,M)$ (or $\\operatorname{Tor}_k^R(L,M)$) and $H_n:=\\operatorname{Ext}^k_R(L, M/I^nN)$ (or $\\operatorname{Tor}_k^R(L,M/I^nN)$). When $I$ is generated by elements of positive degree, we show that the local $v$-number of $H_n$ either coincides with that of colon submodule $(0:_H I)$ or is a polynomial in $n$ of degree one whose leading coefficient is one of the degrees of the generators of $I$. This extends the main result of Ghosh-Pramanik [J. Algebra 671 (2025), 61-74], where asymptotic linearity was shown under the assumption that $(0:_H I)=0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01156",
  "author_total": 3,
  "authors": [
    {
      "name": "Sayed Sadiqul Islam"
    },
    {
      "name": "Lisa Mandal"
    },
    {
      "name": "Samarendra Sahoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0q7v1fh5bpdp1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01156",
  "fulltext_url": null,
  "id": "0q7v1fh5bpdp1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01156",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01156",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0q7v1fh5bpdp1.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01156",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01156"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A study on v-numbers of $\\operatorname{Ext}^i_R(L,M/I^nN)$ and $\\operatorname{Tor}_i^R(L,M/I^nN)$",
  "title_text": "A study on v-numbers of Ext^i_R(L,M/I^nN) and Tor_i^R(L,M/I^nN)",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0q7v1fh5bpdp1",
  "venue": "arXiv",
  "versions": []
}