{
  "abstract": "Let $A$ be an Artin algebra and let $T$ be a self-orthogonal $τ$-tilting right $A$-module. Set $I=\\Ann_A(T)$. We prove that \\[ \\Hom_A(I,T)=0=\\Ext_A^n(I,T)\\qquad(n\\geq 1). \\] It follows that the torsion class generated by $I$ is Hom-orthogonal to $\\Sub T$. This separation yields faithfulness criteria expressed through ideal tops, socles, and projective supports. We also prove a finitistic-dimension obstruction: if $B=\\End_A(T)^{\\rm op}$ has finite little finitistic dimension, then $\\Fac T\\cap{}^{\\perp_{\\geq0}}T=\\{0\\}$. As an application, the self-orthogonal $τ$-tilting conjecture holds for radical square zero Artin algebras. Finally, the support criteria apply to semisimple-source triangular matrix algebras with arbitrary local terminal blocks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27937",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaojin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8q9zzzcypkf5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27937",
  "fulltext_url": null,
  "id": "f8q9zzzcypkf5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27937",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204759237",
  "pdf_url": "https://arxiv.org/pdf/2608.27937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8q9zzzcypkf5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Self-Orthogonal $τ$-Tilting Modules and Tilting Modules II: Annihilator Separation",
  "title_text": "Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/f8q9zzzcypkf5",
  "venue": "arXiv",
  "versions": []
}