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Categorical properties of reduction functors over non-positive DG-rings
- Publication Year :
- 2023
- Publisher :
- American Mathematical Society (AMS), 2023.
-
Abstract
- 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.<br />Comment: 13 pages, final version, to appear in Proceedings of the AMS
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....c36c4ff7118f87304ff97df837103802