Relative quasi-Gorenstein homological dimensions in extriangulated categories

@misc{he2026relative,
  title = {{Relative quasi-Gorenstein homological dimensions in extriangulated categories}},
  author = {Zhenggang He and Jifen Liu and Jiaqun Wei},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01483},
  eprint = {2610.01483},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01483},
}

TY  - UNPB
TI  - Relative quasi-Gorenstein homological dimensions in extriangulated categories
AU  - Zhenggang He
AU  - Jifen Liu
AU  - Jiaqun Wei
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01483
UR  - https://arxiv.org/abs/2610.01483
AB  - Let (𝒞,𝔼,s) be an extriangulated category equipped with a proper class ξ of 𝔼-triangles.We establish stability under iteration for the quasi-ξ-Gorenstein projective and injective subcategories and extend the relative Ext-vanishing criteria for their finite homological dimensions to larger coefficient subcategories. An example in a bounded homotopy category shows that 𝒫(ξ)subsetneq𝒬𝒢𝒫(ξ)subsetneq𝒢𝒫(ξ). For module categories, every quasi-Gorenstein projective module over a left perfect ring or a commutative Noetherian ring of finite Krull dimension is projective. When a commutative ring admits a finite chain of trace and nilpotent quotients ending in an Artinian ring and the endomorphism rings at the trace steps have finite right global dimension, we construct finite families of quasi-projective test modules that detect prescribed upper bounds on projective dimension for modules of bounded cardinality through Ext vanishing in finitely many consecutive degrees.
ER  -