  Given a torsion pair $(\mathcal{T},\mathcal{F})$ in an abelian category
$\mathcal{A}$, there is a t-structure
$(\mathcal{U}_\mathcal{T},\mathcal{V}_\mathcal{T})$ determined by $\mathcal{T}$
on the derived category $D^b(\mathcal{A})$. The existence of derived
equivalence between heart $\mathcal{B}$ of the t-structure and $\mathcal{A}$
which naturally extends the embedding $\mathcal{B}\to D^b(\mathcal{A})$ is
determined by the completeness of the torsion pair [6]. When $\mathcal{A}$ is
the module category of a finite-dimensional hereditary algebra and
$\mathcal{U}_\mathcal{T}$ is closed under Serre functor, then there exists a
triangle equivalence $D^b(\mathcal{B})\to D^b(\mathcal{A})$ [21]. In this case,
we give a straightforward proof of the fact torsion pair
$(\mathcal{T},\mathcal{F})$ is complete if and only if
$\mathcal{U}_\mathcal{T}$ is closed under the Serre functor.
