PreprintCC BY 4.0arXiv
Frobenius functors and n-torsionfree objects
Abstract
We study n-torsionfree objects in abelian categories with enough projectives. Frobenius functors preserve n-torsionfreeness, and faithful ones reflect it. We prove that stabilization of the torsionfree filtration implies weak Gorensteinness. For Frobenius extensions satisfying a generator condition, we compare the terms of minimal injective resolutions and obtain transfer of Auslander-type conditions and of the Auslander--Gorenstein conjecture. We also compute a family of non-Gorenstein algebras whose torsionfree filtrations stabilize at level two and contain explicit nonprojective Gorenstein projective modules.
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BibTeX
@misc{zhao2026frobenius,
title = {{Frobenius functors and $n$-torsionfree objects}},
author = {Zhibing Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25539},
eprint = {2609.25539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25539},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Frobenius functors and n-torsionfree objects
AU - Zhibing Zhao
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.25539
UR - https://arxiv.org/abs/2609.25539
AB - We study n-torsionfree objects in abelian categories with enough projectives. Frobenius functors preserve n-torsionfreeness, and faithful ones reflect it. We prove that stabilization of the torsionfree filtration implies weak Gorensteinness. For Frobenius extensions satisfying a generator condition, we compare the terms of minimal injective resolutions and obtain transfer of Auslander-type conditions and of the Auslander--Gorenstein conjecture. We also compute a family of non-Gorenstein algebras whose torsionfree filtrations stabilize at level two and contain explicit nonprojective Gorenstein projective modules.
ER -