Discreteness of silting objects and t ‐structures in triangulated categories

By T. Adachi, Yuya Mizuno, Dong Ping Yang. Proceedings of the London Mathematical Society, 2017

50 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0312ca04d1b14d0fa9ff4309c1f2f247f127979e