t-structures via recollements for piecewise hereditary algebras

TL;DR

This paper investigates how t-structures in derived categories of piecewise hereditary algebras can be constructed via recollements, providing criteria and showing all bounded t-structures for finite type hereditary algebras arise this way.

Contribution

It establishes a necessary and sufficient condition for inducing t-structures from recollements in derived categories of piecewise hereditary algebras and characterizes all bounded t-structures for finite type hereditary algebras.

Findings

Characterization of when t-structures are induced by recollements

All bounded t-structures for hereditary algebras of finite type are obtained via recollements

Provides a criterion linking t-structures and recollements in derived categories

Abstract

Following the work of Beilinson, Bernstein and Deligne, we study restriction and induction of t-structures in triangulated categories with respect to recollements. For derived categories of piecewise hereditary algebras we give a necessary and sufficient condition for a bounded t-structure to be induced from a recollement by derived categories of algebras. As a corollary we prove that for hereditary algebras of finite representation type all bounded t-structures can be obtained in this way.