On a property of $t$-structures generated by non-classical tilting modules

Abstract

Let R be a ring and T ∈ Mod-R be a (non-classical) tilting module of finite projective dimension. Let T = (T ≤0 , T ≥0 ) be the t-structure on D(R) generated by T and D = (D ≤0 , D ≥0 ) be the natural t-structure. We show that the pair (D, T ) is right filterable in the sense of [FMT14], that is, for any i ∈ Z the intersection D ≥i ∩ T ≥0 is the co-aisle of a t-structure. As a consequence, the heart of T is derived equivalent to Mod-R.