Categorical properties of reduction functors over non-positive DG-rings

Abstract

Given a non-positive DG-ring $A$, associated to it are the reduction and coreduction functors $F(-)={\mathrm{H}}^0(A){\otimes }_A^{\mathrm{L}}-$ and $G(-)=\mathrm{R}{\mathrm{Hom}}_A({\mathrm{H}}^0(A),-)$, considered as functors $D(A)\to D({\mathrm{H}}^0(A))$, as well as the forgetful functor $S:D({\mathrm{H}}^0(A))\to D(A)$. 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 $\mathrm{Ext}$ and $\mathrm{Tor}$ over ordinary commutative noetherian rings is deduced.

13 pages, final version, to appear in Proceedings of the AMS

References in corpus (1)

• Koszul complexes over Cohen-Macaulay rings