Equivariant Matlis and the local duality

TL;DR

This paper extends local duality and Matlis duality to schemes with group actions, providing a broader framework for duality theories in equivariant algebraic geometry.

Contribution

It introduces the first equivariant versions of local duality and Matlis duality, generalizing classical results to schemes with group symmetries.

Findings

Established an equivariant local duality theorem.

Proved an equivariant analogue of Matlis duality.

Extended duality theories to schemes with group actions.

Abstract

Generalizing the known results on graded rings and modules, we formulate and prove the equivariant version of the local duality on schemes with a group action. We also prove an equivariant analogue of Matlis duality.