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Keywords:
silting object; dg-algebra; cosilting dg-module; recollement
silting object; dg-algebra; cosilting dg-module; recollement
Summary:
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.\looseness -1
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