Wakamatsu-silting complexes

We introduce Wakamatsu-silting complexes (resp., Wakamatsu-tilting complexes) as a common generalization of both silting complexes (resp., tilting complexes) and Wakamatsu-tilting modules. Characterizations of Wakamatsu-silting complexes are given. In particular, we show that a complex $T$ is Wakamatsu-silting if and only if its dual $DT$ is Wakamatsu-silting. It is conjectured that all compact Wakamatsu-silting complexes are just silting complexes. We prove that the conjecture lies under the finitistic dimension conjecture.