Ascent and descent of Gorenstein homological properties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909702767509504 |
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| author | Liu, Jian Ren, Wei |
| author_facet | Liu, Jian Ren, Wei |
| contents | Let $φ\colon R\rightarrow A$ 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 $φ$. Finally, we describe when $φ$ induces a triangle equivalence between the stable categories of finitely generated Gorenstein projective modules over $R$ and $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02372 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ascent and descent of Gorenstein homological properties Liu, Jian Ren, Wei Commutative Algebra Rings and Algebras Representation Theory Let $φ\colon R\rightarrow A$ 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 $φ$. Finally, we describe when $φ$ induces a triangle equivalence between the stable categories of finitely generated Gorenstein projective modules over $R$ and $A$. |
| title | Ascent and descent of Gorenstein homological properties |
| topic | Commutative Algebra Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2309.02372 |