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arXiv · 2604.09279

Quasi-projective dimensions of complexes over rings

Hongxing Chen·Jiangsheng Hu·Xiaoyan Yang
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Abstract

Quasi-projective dimension of modules over associative rings is generalized in this paper to the one of complexes of modules. Basic properties of this dimension are established, including a comparison result with projective dimension and a derived Auslander-Buchsbaum formula for complexes of finite quasi-projective dimension. Several sufficient conditions are provided for a commutative noetherian local ring to be a complete intersection under the assumption that each finitely generated module has finite quasi-projective dimension. This provides some positive answers to an open question on quasi-projective dimension proposed by Gheibi-Jorgensen-Takahashi. Moreover, the behavior of quasi-projective dimension under taking the quotient of a commutative ring modulo a regular sequence is investigated, and some partial results toward the change-of-rings question on quasi-projective dimension are given.

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Hongxing Chen, Jiangsheng Hu, Xiaoyan Yang. 2026-04-10. Quasi-projective dimensions of complexes over rings. https://arxiv.org/abs/2604.09279

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