We show that any bounded t-structure in the bounded derived category of a silting-discrete
algebra is algebraic, ie has a length heart with finitely many simple objects. As a corollary …

Bijective correspondences are established between (1) silting objects,(2) simple-minded
collections,(3) bounded $ t $-structures with length heart and (4) bounded co-$ t …

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 …

REPORT ON THE FINITENESS OF SILTING OBJECTS Page 1 Proceedings of the Edinburgh
Mathematical Society (2021) 64, 217–233 doi:10.1017/S0013091521000109 REPORT ON THE …

Discrete derived categories were studied initially by Vossieck ['The algebras with discrete
derived category', J. Algebra 243 (2001) 168–176] and later by Bobiński, Geiß and …

We give examples of finite-dimensional algebras A for which the silting objects in K b (proj-
A) are not connected by any sequence of (possibly reducible) silting mutations. The …

If A is a finite-dimensional symmetric algebra, then it is well-known that the only silting
complexes in K b (proj A) are the tilting complexes. In this note we investigate to what extent …

We study possible values of the global dimension of endomorphism algebras of 2-term
silting complexes. We show that for any algebra A whose global dimension gl. dim A≤ 2 …

First, we give a new example of silting-discrete algebras. Second, one explores when the
algebra of triangular matrices over a finite dimensional algebra is τ-tilting finite. In particular …

We propose the notion of stability on a triangulated category that is a generalization of the T.
Bridgeland's stability data. We establish connections between stabilities and t-structures on …