{
  "abstract": "Let $S$ be a Cohen-Macaulay normal domain containing a field $k$ with an action of a finite group $G$ with $|G|$ invertible in $k$. We prove that $G$-equivariant noncommutative crepant resolutions of $S$ induce noncommutative crepant resolutions of $S^G$ if the $G$-action is small. We also discuss similar results for equivariant maximal modification algebras. We introduce the notion of $G$-maximal modifying ($G$-MM) module, and we show that $G$-MM module over $S$ induces MM $S^G$-module in some special cases. Furthermore, we prove that Gorenstein MMAs of three-dimensional $\\mathbb{Q}$-Gorenstein Cohen-Macaulay rings are derived equivalent. As an application of these results, we prove the existence of an MM module and derived equivalences of MMAs for three-dimensional terminal singularities of index two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11708",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuki Hirano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9xzm8jb80j7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11708",
  "fulltext_url": null,
  "id": "f9xzm8jb80j7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11708",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221084189",
  "pdf_url": "https://arxiv.org/pdf/2610.11708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f9xzm8jb80j7w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.11708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Equivariant noncommutative crepant resolutions and $G$-maximal modifying modules",
  "title_text": "Equivariant noncommutative crepant resolutions and G-maximal modifying modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/f9xzm8jb80j7w",
  "venue": "arXiv",
  "versions": []
}