{
  "abstract": "We study equivalences between quotient categories of module categories associated with Gabriel topologies. We establish necessary and sufficient conditions for a Morita context to induce an equivalence between quotient categories and characterize such equivalences in terms of Morita contexts after passing to rings of quotients. Motivated by Artin--Zhang's noncommutative Serre theorem, we introduce a notion of ampleness relative to a Gabriel topology and use it to characterize quotient categories of finitely generated modules under suitable noetherian hypotheses. As an application, we establish a sufficient condition under which the noncommutative Auslander theorem holds for actions of finite-dimensional Hopf algebras on AS-regular algebras without assuming that the Hopf algebras are semisimple.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39160",
  "author_total": 3,
  "authors": [
    {
      "name": "Xuyang Chen"
    },
    {
      "name": "Haonan Li"
    },
    {
      "name": "Quanshui Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hrny2764cdkj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39160",
  "fulltext_url": null,
  "id": "7hrny2764cdkj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39160",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7215120352",
  "pdf_url": "https://arxiv.org/pdf/2609.39160",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hrny2764cdkj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39160",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39160"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quotient Morita Theory with Applications",
  "title_text": "Quotient Morita Theory with Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/7hrny2764cdkj",
  "venue": "arXiv",
  "versions": []
}