Derived equivalences for hereditary Artin algebras

We study the role of the Serre functor in the theory of derived equivalences. Let $\mathcal{A}$ be an abelian category and let $(\mathcal{U},\mathcal{V})$ be a $t$-structure on the bounded derived category $D^b\mathcal{A}$ with heart $\mathcal{H}$. We investigate when the natural embedding $$\mathcal{H}$ \to D^b $\mathcal{A}$$canbeextendedtoatriangleequivalence$D^b $\mathcal{H}$ \to D^b $\mathcal{A}$$\mathrm{.}Ourfocusofstudyisthecasewhere$$\mathcal{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 $\mathcal{U}$ of the $t$-structure is closed under the Serre functor.