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 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 a 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.

41 pages. Typos corrected. To appear in PLMS

References in corpus (3)

• Calabi-Yau algebras
• Universal localisations via silting
• Gopakumar-Vafa invariants do not determine flops

Cited by in corpus (8)

• Silting objects
• Reductions of triangulated categories and simple-minded collections
• Gluing simple-minded collections in triangulated categories
• From simple-minded collections to silting objects via Koszul duality
• Examples of tilting-discrete self-injective algebras which are not silting-discrete
• The ST correspondence for proper non-positive dg algebras
• Derived projective covers and Koszul duality of simple-minded and silting collections
• Fishing for complements