Categorical properties of reduction functors over non-positive DG-rings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910287515353088 |
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| author | Shaul, Liran |
| author_facet | Shaul, Liran |
| contents | Given a non-positive DG-ring $A$, associated to it are the reduction and coreduction functors $F(-) = \mathrm{H}^0(A)\otimes^{\mathrm{L}}_A -$ and $G(-) = \mathrm{R}\operatorname{Hom}_A(\mathrm{H}^0(A),-)$, considered as functors $\operatorname{\mathsf{D}}(A) \to \operatorname{\mathsf{D}}(\mathrm{H}^0(A))$, as well as the forgetful functor $S:\operatorname{\mathsf{D}}(\mathrm{H}^0(A)) \to \operatorname{\mathsf{D}}(A)$. In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of $\operatorname{Ext}$ and $\operatorname{Tor}$ over ordinary commutative noetherian rings is deduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07348 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Categorical properties of reduction functors over non-positive DG-rings Shaul, Liran Rings and Algebras Commutative Algebra Category Theory Primary: 16E45, Secondary: 18A22, 13D07, 13D09 Given a non-positive DG-ring $A$, associated to it are the reduction and coreduction functors $F(-) = \mathrm{H}^0(A)\otimes^{\mathrm{L}}_A -$ and $G(-) = \mathrm{R}\operatorname{Hom}_A(\mathrm{H}^0(A),-)$, considered as functors $\operatorname{\mathsf{D}}(A) \to \operatorname{\mathsf{D}}(\mathrm{H}^0(A))$, as well as the forgetful functor $S:\operatorname{\mathsf{D}}(\mathrm{H}^0(A)) \to \operatorname{\mathsf{D}}(A)$. In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of $\operatorname{Ext}$ and $\operatorname{Tor}$ over ordinary commutative noetherian rings is deduced. |
| title | Categorical properties of reduction functors over non-positive DG-rings |
| topic | Rings and Algebras Commutative Algebra Category Theory Primary: 16E45, Secondary: 18A22, 13D07, 13D09 |
| url | https://arxiv.org/abs/2210.07348 |