Discreteness of silting objects and t-structures in triangulated categories

Abstract

We introduce the notion of ST-pairs of triangulated subcategories, a prototypical example of which is the pair of the bound homotopy category and the bound derived category of a finite-dimensional algebra. For an ST-pair ( C , D ) , we construct an injective order-preserving map from silting objects in C to bounded t-structures on D and show that the map is bijective if and only if C is silting-discrete if and only if D is t-discrete. Based on the work of Qiu and Woolf, the above result is applied to show that if C is silting-discrete then the stability space of D is contractible. This is used to obtain the contractibility of the stability spaces of some Calabi–Yau triangulated categories associated to Dynkin quivers.