Derived equivalences for hereditary Artin algebras

Abstract

We study the role of the Serre functor in the theory of derived equivalences. Let A be an abelian category and let (U,V) be a t-structure on the bounded derived category DbA with heart H. We investigate when the natural embedding H→DbA can be extended to a triangle equivalence DbH→DbA. Our focus of study is the case where A is the category of finite-dimensional modules over a finite-dimensional hereditary algebra. In this case, we prove that such an extension exists if and only if the t-structure is bounded and the aisle U of the t-structure is closed under the Serre functor.