Glueing silting objects

Recent results by Keller and Nicol{\'a}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other hand, the techniques of glueing (co-)t-structures along a recollement play an important role in the understanding of derived module categories. Using the above correspondence with silting objects we present explicit constructions of glueing of silting objects, and, furthermore, we answer the question of when is the glued silting tilting

Classifying tt-structures via ICE-closed subcategories and a lattice of torsion classes

In a triangulated category equipped with a $t$-structure, we investigate a relation between ICE-closed (=Image-Cokernel-Extension-closed) subcategories of the heart of the $t$-structure and aisles in the triangulated categories. We introduce an ICE sequence, a sequence of ICE-closed subcategories satisfying a certain condition, and establish a bijection between ICE sequences and homology-determined preaisles. Moreover we give a sufficient condition that an ICE sequence induces a $t$-structure via the bijection. In the case of the bounded derived category $D^b({\mathsf{mod}}\Lambda)$ of a $\tau$-tilting finite algebra $\Lambda$, we give a description of ICE sequences in ${\mathsf{mod}}\Lambda$ which induce bounded $t$-structures on $D^b({\mathsf{mod}}\Lambda)$ from the viewpoint of a lattice consisting of torsion classes in ${\mathsf{mod}}\Lambda$.Comment: 16 page