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PreprintarXiv licencearXiv

On the homological conjectures for Artin algebras

  • Haruhisa Enomoto
  • Rene Marczinzik
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Abstract

We prove that the Auslander--Reiten conjecture, the generalised Nakayama conjecture, the Nakayama conjecture, and each of the two Tachikawa conjectures are globally equivalent for Artin algebras over any fixed commutative artinian ring. For finite dimensional algebras over a fixed field, we also prove that the derived invariance of the Nakayama conjecture is equivalent to the truth of the Nakayama conjecture for all such algebras, answering a question raised by Chen and Xi.

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Cite

BibTeXRIS
BibTeX
@misc{enomoto2026homological,
  title = {{On the homological conjectures for Artin algebras}},
  author = {Haruhisa Enomoto and Rene Marczinzik},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19172},
  eprint = {2609.19172},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19172},
}
RIS
TY  - UNPB
TI  - On the homological conjectures for Artin algebras
AU  - Haruhisa Enomoto
AU  - Rene Marczinzik
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.19172
UR  - https://arxiv.org/abs/2609.19172
AB  - We prove that the Auslander--Reiten conjecture, the generalised Nakayama conjecture, the Nakayama conjecture, and each of the two Tachikawa conjectures are globally equivalent for Artin algebras over any fixed commutative artinian ring. For finite dimensional algebras over a fixed field, we also prove that the derived invariance of the Nakayama conjecture is equivalent to the truth of the Nakayama conjecture for all such algebras, answering a question raised by Chen and Xi.
ER  -