{
  "abstract": "Let $U$ be a support $τ$-tilting module over a finite dimensional algebra $A$, and let $\\mathcal{V}\\subseteq \\text{Fac}U$ be any torsion class. The heart $\\mathcal H=\\text{Fac} U\\cap \\mathcal{V}^\\perp$ inherits the exact structure from mod$A$ and admits an Ext-progenerator $P$. Let $B=\\text{End}_A(P)$. We define the relative derived delooping level on the exact heart $\\mathcal H$ and compare it with the relative delooping level on $\\mathcal {H}$ and the derived delooping level of $B$. We show that $\\text{Findim} B^{op}$ is bounded by the relative derived delooping level on the $\\mathcal H$. For a wide heart, the relative derived delooping level on the heart equals the derived delooping level of $B$. We obtain explicit bounds from representation-finite relative syzygy strata and characterize global first-order finiteness using an Ext-injective cogenerator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37050",
  "author_total": 1,
  "authors": [
    {
      "name": "Weiqing Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afn428p8wyxxc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37050",
  "fulltext_url": null,
  "id": "afn428p8wyxxc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37050",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7224084961",
  "pdf_url": "https://arxiv.org/pdf/2610.37050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afn428p8wyxxc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Relative derived delooping levels and torsion intervals",
  "title_text": "Relative derived delooping levels and torsion intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/afn428p8wyxxc",
  "venue": "arXiv",
  "versions": []
}