{
  "abstract": "We introduce the global obstruction property (GOP) for Artin algebras: for every finitely generated module of infinite projective dimension, two distinct syzygies have a common nonprojective indecomposable direct summand. We prove that GOP implies the generalized Auslander--Reiten condition, and hence the Auslander--Reiten conjecture. We give criteria for GOP to hold for pullbacks over semisimple algebras and construct an example which is not syzygy-finite. For each Artin algebra $A$, we construct an algebra $\\mathcal{G}(A)$ satisfying GOP by using triangular matrix extensions. We show that $\\text{fin.dim}\\mathcal{G}(A)=\\text{fin.dim} A+2$ and that $A$ and $\\mathcal{G}(A)$ are singularly equivalent. Finally, we give a pair of derived equivalent finite-dimensional algebras for which GOP holds on only one side.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12583",
  "author_total": 1,
  "authors": [
    {
      "name": "Weiheng Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zzhycsc75ajp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12583",
  "fulltext_url": null,
  "id": "5zzhycsc75ajp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12583",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221537172",
  "pdf_url": "https://arxiv.org/pdf/2610.12583",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zzhycsc75ajp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12583",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12583"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Global obstruction property and its applications",
  "title_text": "Global obstruction property and its applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/5zzhycsc75ajp",
  "venue": "arXiv",
  "versions": []
}