{
  "abstract": "Let $A$ be an Artin algebra and let $T$ be a $τ$-tilting right $A$-module. Put $C=A/{\\rm Ann}_A(T)$. We prove that finite little finitistic dimension of $C^{\\rm op}$, together with a finite range of self-extension vanishing for $T$, forces $T$ to be a classical $1$-tilting module. We also show that if the finitistic conjecture holds for all Artin algebras then the self-orthogonal $τ$-tilting conjecture holds for all Artin algebras. Moreover, a counterexample to the self-orthogonal $τ$-tilting conjecture will give a counterexample to the finitistic dimension conjecture. As an application, the self-orthogonal $τ$-tilting conjecture holds for Artin algebras with radical cube zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00105",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaojin Zhang"
    },
    {
      "name": "Panyue Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a11hjn10rzgfz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00105",
  "fulltext_url": null,
  "id": "a11hjn10rzgfz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00105",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7216330127",
  "pdf_url": "https://arxiv.org/pdf/2610.00105",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a11hjn10rzgfz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00105",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00105"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Self-Orthogonal $τ$-Tilting Modules and Tilting Modules III: Finitistic Dimension",
  "title_text": "Self-Orthogonal τ-Tilting Modules and Tilting Modules III: Finitistic Dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/a11hjn10rzgfz",
  "venue": "arXiv",
  "versions": []
}