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arXiv · 1708.08168

Discreteness of silting objects and t-structures in triangulated categories

Takahide Adachi·Yuya Mizuno·Dong Yang
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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.

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Takahide Adachi, Yuya Mizuno, Dong Yang. 2017-08-28. Discreteness of silting objects and t-structures in triangulated categories. https://doi.org/10.1112/plms.12176

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