{
  "abstract": "Keller's strong form of the homological conjectures asserts: any finite dimensional algebra cogenerates its unbounded derived category of modules. Here we record an example of a (coconnective) dg algebra with finite dimensional cohomology, which does not cogenerate its module category, along with some related phenomena: a smooth dg category whose dualizing bimodule fails to be nondegenerate, and a nontrivial fully faithful left Calabi-Yau morphism. All examples and most proofs were produced by ChatGPT. In an appendix we explain the reason we were looking for such examples: their existence would follow from the existence of Weinstein symplectic manifolds which failed to satisfy Arnol'd's chord conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34193",
  "author_total": 3,
  "authors": [
    {
      "name": "Mingyuan Hu"
    },
    {
      "name": "Vivek Shende"
    },
    {
      "name": "Dinglong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/259g10g4thhy0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34193",
  "fulltext_url": null,
  "id": "259g10g4thhy0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34193",
  "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.SG"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214799446",
  "pdf_url": "https://arxiv.org/pdf/2609.34193",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/259g10g4thhy0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34193",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34193"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A proper dg algebra which does not cogenerate",
  "title_text": "A proper dg algebra which does not cogenerate",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/259g10g4thhy0",
  "venue": "arXiv",
  "versions": []
}