{
  "abstract": "Let $(A,\\mathfrak{m})$ be a Noetherian local ring and let $I\\subseteq \\mathfrak{m}$ be an ideal in $A$. Let $\\ell(I)$ be the analytic spread of $I$. Let $G_I(A) = \\bigoplus_{n \\geq 0}I^n/I^{n+1}$ be the associated graded ring of $I$ and let its depth be $t$. We prove $\\text{depth} \\ A/I^n \\geq t - \\ell(I)$ for all $n\\geq 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14973",
  "author_total": 1,
  "authors": [
    {
      "name": "Tony J. Puthenpurakal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fkzn646nb9k1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14973",
  "fulltext_url": null,
  "id": "2fkzn646nb9k1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14973",
  "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": "W7221824630",
  "pdf_url": "https://arxiv.org/pdf/2610.14973",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fkzn646nb9k1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14973",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14973"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A lower bound on $\\text{depth} \\ \\mathbf{A/I^n}$",
  "title_text": "A lower bound on depth A/I^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2fkzn646nb9k1",
  "venue": "arXiv",
  "versions": []
}