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 -> D(b)A can be extended to a triangle equivalence (DH)-H-b -> D(b)A. 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. (C) 2016 Elsevier Inc. All rights reserved.