Czechoslovak Mathematical Journal, Vol. 73, No. 2, pp. 453-473, 2023
Recollements induced by good (co)silting dg-modules
Rongmin Zhu, Jiaqun Wei
Received October 2, 2021. Published online February 8, 2023.
Abstract: Let $U$ be a dg-$A$-module, $B$ the endomorphism dg-algebra of $U$. We know that if $U$ is a good silting object, then there exist a dg-algebra $C$ and a recollement among the derived categories ${\mathbf D}(C,d)$ of $C$, ${\mathbf D}(B,d)$ of $B$ and ${\mathbf D}(A,d)$ of $A$. We investigate the condition under which the induced dg-algebra $C$ is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained. Finally, some applications are given related to good 2-term silting complexes, good tilting complexes and modules.
Affiliations: Rongmin Zhu (corresponding author), School of Mathematical Sciences, Huaqiao University, No.269 Chenghua North Road, Quanzhou 362021, P. R. China, e-mail: rongminzhu@hotmail.com; Jiaqun Wei, School of Mathematics Sciences, Nanjing Normal University, No.1 Wenyuan Road, Nanjing 210023, P. R. China, e-mail: weijiaqun@njnu.edu.cn
