On the homological conjectures for Artin algebras
Updated:
(joint work with Rene Marczinzik)
arXiv preprint, September 2026. Link: arXiv:2609.19172
Citation: H. Enomoto, R. Marczinzik, On the homological conjectures for Artin algebras, arXiv:2609.19172.
Comment
For Artin algebras over a fixed commutative artinian ring, we establish global equivalence of the Auslander-Reiten conjecture, the generalised Nakayama conjecture, the Nakayama conjecture, and both Tachikawa conjectures.
For finite-dimensional algebras over a fixed field, we also show that derived invariance of the Nakayama conjecture is equivalent to its validity for all such algebras, answering a question of Chen and Xi.
Version 2 adds Rene Marczinzik as co-author and expands the results of the first version, which was titled “Tachikawa’s second conjecture implies the Auslander-Reiten conjecture”.
Version 2 was submitted to arXiv on September 24, 2026.