Dualities of artinian coalgebras with applications to noetherian complete algebras

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 ${}_1C_{σ^*}$ with $σ$ a coalgebra automorphism. This yields that the balanced dualinzing complex of $A$ is a shift of the twisted bimodule ${}_{σ^*}A_1$. If $σ$ is an inner automorphism, then $A$ is Calabi-Yau.

No reviews yet.

No comments yet.