{
  "abstract": "We prove new cases of the Auslander-Reiten conjecture under the assumption that the base ring satisfies the totally acyclic condition $(\\mathbf{tac})$. A consequence of our work is that Auslander-Reiten conjecture holds in the graded setting whenever $R$ is Gorenstein and reduced. We also give an example of a local ring $R$ which does not satisfy $(\\mathbf{tac})$ but for which the condition $\\operatorname{Ext}^{i>0}_R(M,R)=0$ implies $M$ is totally reflexive for any finitely generated $R$-module $M$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00022",
  "author_total": 1,
  "authors": [
    {
      "name": "Justin Lyle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etttp99z0468d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00022",
  "fulltext_url": null,
  "id": "etttp99z0468d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00022",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7216390979",
  "pdf_url": "https://arxiv.org/pdf/2610.00022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etttp99z0468d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00022"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the totally acyclic condition and the Auslander-Reiten Conjecture",
  "title_text": "On the totally acyclic condition and the Auslander-Reiten Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/etttp99z0468d",
  "venue": "arXiv",
  "versions": []
}