A duality theorem of the bounded derived category of quasi-finite comodules
over an artinian coalgebra is established. Let $A$ be a noetherian complete
basic semiperfect algebra over an algebraically closed field, and $C$ be its
dual coalgebra. If $A$ is Artin-Schelter regular, then the local cohomology of
$A$ is isomorphic to a shift of twisted bimodule ${}_1C_{\sigma^*}$ with
$\sigma$ a coalgebra automorphism. This yields that the balanced dualinzing
complex of $A$ is a shift of the twisted bimodule ${}_{\sigma^*}A_1$. If
$\sigma$ is an inner automorphism, then $A$ is Calabi-Yau.