Derived equivalences induced by good silting complexes (Q6617855)

The derived category is the smallest additive category that transforms a quasi-isomorphism into an isomorphism, and the extensive related study on it is highly meaningful. The classical tilting theory is well known, and plays an important role in the representation theory of Artin algebras. The authors in the present paper under review explored the equivalences induced by some special silting objects in the derived category over dg-algebra whose positive cohomologies are all zero. Specifically, they considered some special silting objects, called silting complexes, in the derived category associated to a coconnective dg-algebra. In this way, they extended the semi-tilting complexes defined by \textit{J. Wei} [Isr. J. Math. 194, Part B, 871--893 (2013; Zbl 1286.16011)]. they proved that these objects are always equivalent to some complexes, called good, that satisfy some special hypotheses. They also applied their results in order to obtain some counter equivalences for good silting complexes, similar to the tilting case. In fact, their results in this paper generalized the results involving (derived) equivalences for tilting complexes by \textit{S. Bazzoni} et al. [Proc. Am. Math. Soc. 139, No. 12, 4225--4234 (2011; Zbl 1232.16004)].\N\NFor the entire collection see [Zbl 1539.13002].