{
  "abstract": "Let $R$ be a commutative noetherian local ring with residue field $k$. Denote by $\\operatorname{\\mathsf{D^b}}(R)$ the bounded derived category of finitely generated $R$-modules. In this paper, we introduce the notion of ranks of triangulated categories and study Verdier quotients of $\\operatorname{\\mathsf{D^b}}(R)$ from the viewpoint of this invariant. Our main result determines the rank of the Verdier quotient $\\operatorname{\\mathsf{D^b}}(R)/\\operatorname{\\mathsf{thick}}(R\\oplus k)$ in terms of the ranks of the categories of maximal Cohen-Macaulay modules on the punctured spectrum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06456",
  "author_total": 2,
  "authors": [
    {
      "name": "Souvik Dey"
    },
    {
      "name": "Yuki Mifune"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb3vcef474t4x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06456",
  "fulltext_url": null,
  "id": "cb3vcef474t4x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06456",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212086960",
  "pdf_url": "https://arxiv.org/pdf/2609.06456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb3vcef474t4x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06456"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ranks of Verdier quotients of derived categories over local rings",
  "title_text": "Ranks of Verdier quotients of derived categories over local rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cb3vcef474t4x",
  "venue": "arXiv",
  "versions": []
}