Derived equivalences via HRS-tilting

Abstract

Let $\mathcal{A}$ be an abelian category and $\mathcal{B}$ be the Happel-Reiten-Smal{\o} tilt of $\mathcal{A}$ with respect to a torsion pair. We give necessary and sufficient conditions for the existence of a derived equivalence between $\mathcal{B}$ and $\mathcal{A}$, which is compatible with the inclusion of $\mathcal{B}$ into the derived category of $\mathcal{A}$. In particular, any splitting torsion pair induces a derived equivalence. We prove that for the realization functor of any bounded $t$-structure, its denseness implies its fully-faithfulness.