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Auslander-type grade conditions and subcategories related to syzygy modules

  • Yuya Otake
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Abstract

The question of when a syzygy module or a module satisfying a Serre condition satisfies the cohomological vanishing conditions known as higher torsionfreeness has been extensively studied. In this paper, we address these questions using grade conditions introduced and studied by Auslander-Bridger and Auslander-Reiten. We also investigate homological conditions on Ext modules and, as an application, give a partial answer over commutative rings to a question of Auslander-Bridger concerning whether higher reflexive modules are higher torsionfree.

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Cite

BibTeXRIS
BibTeX
@misc{otake2026auslandertype,
  title = {{Auslander-type grade conditions and subcategories related to syzygy modules}},
  author = {Yuya Otake},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00913},
  eprint = {2611.00913},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00913},
}
RIS
TY  - UNPB
TI  - Auslander-type grade conditions and subcategories related to syzygy modules
AU  - Yuya Otake
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00913
UR  - https://arxiv.org/abs/2611.00913
AB  - The question of when a syzygy module or a module satisfying a Serre condition satisfies the cohomological vanishing conditions known as higher torsionfreeness has been extensively studied. In this paper, we address these questions using grade conditions introduced and studied by Auslander-Bridger and Auslander-Reiten. We also investigate homological conditions on Ext modules and, as an application, give a partial answer over commutative rings to a question of Auslander-Bridger concerning whether higher reflexive modules are higher torsionfree.
ER  -