Recollements induced by good (co)silting dg-modules

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 D(C, d) of C, D(B, d) of B and 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.