Silting objects under special base changes

Abstract

Let A be a ring. In this paper we study the behavior of silting objects in derived categories of module categories under special base changes with respect to the rings $A_x$ and $A/xA$, where x is a regular element in A. We prove that any silting object in $D\left(A\right)$ gives rise to silting objects in $D\left(A_x\right)$ and $D(A/xA)$ after localization and passing to quotient, respectively. On the other hand, it is proved that under some mild conditions, an object in $D\left(A\right)$ is silting if its corresponding localization and quotient are silting in $D\left(A_x\right)$ and $D(A/xA)$, respectively.