Homotopy equivalences and Grothendieck duality over rings with finite Gorenstein weak global dimension
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913223195754496 |
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| author | Wang, Junpeng Estrada, Sergio |
| author_facet | Wang, Junpeng Estrada, Sergio |
| contents | Let $R$ be a ring with Gwgldim$(R)<\infty$. We obtain a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{GProj})\simeq \mathrm{K}(R\text{-}\mathrm{GInj})$ which restricts to a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{Proj})$ $\simeq \mathrm{K}(R\text{-}\mathrm{Inj})$. This class of rings includes, among others, (left) Gorenstein rings, Ding-Chen rings and the more general Gorenstein $n$-coherent rings ($n\in \mathbb{N}\cup \{\infty\}, n\geq 2$). As application, we establish some triangle-equivalences of Grothendieck duality over Ding-Chen rings and Gorenstein $n$-coherent rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy equivalences and Grothendieck duality over rings with finite Gorenstein weak global dimension Wang, Junpeng Estrada, Sergio Rings and Algebras Let $R$ be a ring with Gwgldim$(R)<\infty$. We obtain a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{GProj})\simeq \mathrm{K}(R\text{-}\mathrm{GInj})$ which restricts to a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{Proj})$ $\simeq \mathrm{K}(R\text{-}\mathrm{Inj})$. This class of rings includes, among others, (left) Gorenstein rings, Ding-Chen rings and the more general Gorenstein $n$-coherent rings ($n\in \mathbb{N}\cup \{\infty\}, n\geq 2$). As application, we establish some triangle-equivalences of Grothendieck duality over Ding-Chen rings and Gorenstein $n$-coherent rings. |
| title | Homotopy equivalences and Grothendieck duality over rings with finite Gorenstein weak global dimension |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.03010 |