Equivariant noncommutative crepant resolutions and G-maximal modifying modules

@misc{hirano2026equivariant,
  title = {{Equivariant noncommutative crepant resolutions and $G$-maximal modifying modules}},
  author = {Yuki Hirano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11708},
  eprint = {2610.11708},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11708},
}

TY  - UNPB
TI  - Equivariant noncommutative crepant resolutions and G-maximal modifying modules
AU  - Yuki Hirano
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.11708
UR  - https://arxiv.org/abs/2610.11708
AB  - 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 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.
ER  -