{
  "abstract": "The notion of $d$-stable dg categories axiomatizes $d$-cluster tilting subcategories of stable dg categories. We establish an Auslander correspondence for $d$-stable dg categories: we characterize the $d$-stability of an additive connective dg category in terms of coherence, weak global dimension, and a duality on finitely presented modules. This gives a homological characterization of $d$-stability and reveals it as a twisted form of $(d+1)$-Calabi--Yau duality. For locally finite connective dg algebras, this interpretation becomes particularly transparent under Koszul duality, where $d$-stability corresponds to a shifted self-injectivity condition on the Koszul dual. Following the constructions of Amiot, Guo and Keller, for a $d$-stable dg category $M$, we introduce its $d$-cluster dg category $\\mathcal C_{d,{\\rm dg}}(M):=\\operatorname{per}_{\\rm dg}M/^\\mathbb{L}\\mathcal D^b_{\\rm fp, dg}(M)$. Using our Auslander correspondence, we show that $\\mathcal C_{d,{\\rm dg}}(M)$ contains $M$ as a $d$-cluster tilting subcategory. In particular, every $d$-stable dg category can be realized as a $d$-cluster tilting subcategory of a stable dg category. We then develop cluster Morita theory: a pretriangulated dg category equipped with a $d$-cluster tilting subcategory $M$ is quasi-equivalent to $\\mathcal C_{d,{\\rm dg}}(M)$. Thus the connective dg structure of a cluster tilting subcategory determines its ambient dg category up to quasi-equivalence. As an application of cluster Morita theory, we prove a Morita-theoretic variant of Amiot's conjecture. More precisely, we establish a Calabi--Yau correspondence: for a locally finite $d$-stable dg category $M$ over a field, right $(d+1)$-Calabi--Yau structures on $\\mathcal D^b_{\\rm fp, dg}(M)$ are in bijection with right $d$-Calabi--Yau structures on $\\mathcal C_{d,{\\rm dg}}(M)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30740",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryu Tomonaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3489js1dj57p8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30740",
  "fulltext_url": null,
  "id": "3489js1dj57p8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30740",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204920069",
  "pdf_url": "https://arxiv.org/pdf/2608.30740",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3489js1dj57p8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30740",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30740"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Auslander correspondence for higher stable dg categories and cluster Morita theory",
  "title_text": "Auslander correspondence for higher stable dg categories and cluster Morita theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/3489js1dj57p8",
  "venue": "arXiv",
  "versions": []
}