论文标题
在非阳性DG环上还原函子的分类特性
Categorical properties of reduction functors over non-positive DG-rings
论文作者
论文摘要
给定一个非阳性dg-ring $ a $，与之相关的是减少和加油函数$ f（ - ）= \ mathrm {h}^0（a）\ otimes^{\ mathrm {l}} _ a - a- $ $ g（ - ）= - 和$ g（ - ）= \ Mathrm {r} \ protatorName {hom} _a（\ Mathrm {h}^0（a）， - ）$，被视为函数$ \ peripatorName {\ mathsf {d}}}（d}}}（a）\ to \ operatornAme {健忘的函数$ s：\ operatorAtorName {\ mathsf {d}}（\ mathrm {h}^0（a））\ to \ operatoTorname {\ mathsf {d}}}（a）$。在本文中，我们对这些函子的分类特性进行了系统的研究。作为一个应用程序，推导了$ \ operatorname {ext} $和$ \ operatatorName {tor} $在普通交换Noetherian戒指上的新下降结果。
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.
