  For a finite-dimensional algebra $\Lambda$ over an algebraically closed field
$K$, it is known that the poset of $2$-term silting objects in
$\mathrm{K}^b(\operatorname{proj}\Lambda)$ is isomorphic to the poset of
functorially finite torsion classes in $\operatorname{mod}\Lambda$, and to that
of complete cotorsion classes in
$\mathrm{K}^{[-1,0]}(\operatorname{proj}\Lambda)$. In this work, we generalise
this result to the case of $d$-term silting objects for arbitrary $d\geq 2$ by
introducing the notion of torsion classes for extriangulated categories. In
particular, we show that the poset of $d$-term silting objects in
$\mathrm{K}^b(\operatorname{proj}\Lambda)$ is isomorphic to the poset of
complete and hereditary cotorsion classes in
$\mathrm{K}^{[-d+1,0]}(\operatorname{proj}\Lambda)$, and to that of positive
and functorially finite torsion classes in
$D^{[-d+2,0]}(\operatorname{mod}\Lambda)$, an extension-closed subcategory of
$D^b(\operatorname{mod}\Lambda)$. We further show that the posets
$\operatorname{cotors}\mathrm{K}^{[-d+1,0]}(\operatorname{proj}\Lambda)$ and
$\operatorname{tors} D^{[-d+2,0]}(\operatorname{mod}\Lambda)$ are lattices, and
that the truncation functor $\tau_{\geq -d+2}$ gives an isomorphism between the
two.
