On the totally acyclic condition and the Auslander-Reiten Conjecture

@misc{lyle2026totally,
  title = {{On the totally acyclic condition and the Auslander-Reiten Conjecture}},
  author = {Justin Lyle},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00022},
  eprint = {2610.00022},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00022},
}

TY  - UNPB
TI  - On the totally acyclic condition and the Auslander-Reiten Conjecture
AU  - Justin Lyle
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00022
UR  - https://arxiv.org/abs/2610.00022
AB  - We prove new cases of the Auslander-Reiten conjecture under the assumption that the base ring satisfies the totally acyclic condition (tac). A consequence of our work is that Auslander-Reiten conjecture holds in the graded setting whenever R is Gorenstein and reduced. We also give an example of a local ring R which does not satisfy (tac) but for which the condition Ext^i>0_R(M,R)=0 implies M is totally reflexive for any finitely generated R-module M.
ER  -