Discreteness of silting objects and t-structures in triangulated categories

2017/08/31 by Takahide Adachi, Yuya Mizuno, Dong Yang · 1 citation
Mathematics · #math.CT #math.RT #msc:16E35 #msc:16E45 #msc:18E30

paper · pdf · doi:10.1112/plms.12176

41 pages. Typos corrected. To appear in PLMS

arxiv created 2018/06/07 · arxiv updated 2018/08/01

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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• Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings

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