Tuesday, May 6, 14:00, 7.527.

Junhua Zheng
Lifting and restricting t-structures in weakly approximable triangulated categories.

Abstract:
The notation of weakly approximable triangulated category was firstly introduced by Amnon Neeman in 2018, which is a special kind of compactly generated triangulated category. In a weakly approximable triangulated category Τ, there exists another full subcategory, consisting of bounded pseudo-compact objects, which is denoted by Τ^b_c. A typical example arises when Τ = D(Mod-R) for a ring R, in which case Τ^b_c coincides with K^-,b(proj-R).

Inspired by the work of Marks and Zvonareva, who established a bijection between certain classes of bounded t-structures on D^b(mod-R) and D(Mod-R) for a coherent ring R, we construct a similar correspondence between specific t-structures on Τ^b_c and those on Τ.

As a application, we will talk about the existence of bounded t-structures on Τ. In particular, we get the following statement: for a finite dimensional k-algebra A, K^b(proj-A) has a bounded t-structure if and only if the global dimensional of A is finite.

This talk is based on joint work with Xiaohu Chen.