Ascent and descent of Gorenstein homological properties

Jian Liu; Wei Ren

doi:10.1016/j.jpaa.2025.108042

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arXiv · 2309.02372

Ascent and descent of Gorenstein homological properties

Jian Liu·Wei Ren

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Abstract

Let $\varphi\colon R\rightarrow A$ be a ring homomorphism, where $R$ is a commutative noetherian ring and $A$ is a finite $R$-algebra. We provide criteria for detecting the ascent and descent of Gorenstein homological properties. %As an application, one can deduce a result that supports a question of Avramov and Foxby. We observe that the ascent and descent of Gorenstein homological property can detect the Gorenstein properties of rings along $\varphi$. Finally, we describe when $\varphi$ induces a triangle equivalence between the stable categories of finitely generated Gorenstein projective modules over $R$ and $A$.

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Jian Liu, Wei Ren. 2023-09-05. Ascent and descent of Gorenstein homological properties. https://doi.org/10.1016/j.jpaa.2025.108042

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