Singular equivalences of n-adjoint type and standard eventually homological isomorphisms

@misc{han2026singular,
  title = {{Singular equivalences of $n$-adjoint type and standard eventually homological isomorphisms}},
  author = {Yang Han and Yongyun Qin and Xianqing Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.03365},
  eprint = {2609.03365},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03365},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Singular equivalences of n-adjoint type and standard eventually homological isomorphisms
AU  - Yang Han
AU  - Yongyun Qin
AU  - Xianqing Wang
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.03365
UR  - https://arxiv.org/abs/2609.03365
AB  - We refine the definition of eventually homological isomorphisms so that it becomes more natural and fruitful. We introduce singular equivalences of n-adjoint type which can be viewed as standard singular equivalences of different levels and are more convenient for reducing various homological conjectures and transferring homological properties. We develop the theories of singular equivalences of n-adjoint type for n≥ 2 and standard eventually homological isomorphisms between derived categories by giving their characterizations in terms of ⊗-(co)perfect complexes of bimodules, two constructions via opposite algebras and tensor product algebras, examples induced by homomorphisms of algebras and idempotents, and applications to the reduction of homological conjectures such as the finitistic dimension conjecture, Gorenstein symmetry conjecture and Auslander-Reiten conjecture, as well as to the preservation of homological properties such as Gorensteinness, the Fg condition, Happel's property and Han's property. Moreover, we show that essentially surjective standard eventually homological isomorphisms between derived categories correspond to standard singular equivalences with canonical left adjoint.
ER  -