A duality theorem for generalized local cohomology

TL;DR

This paper establishes a duality theorem for generalized local cohomology in graded algebras, unifying several existing duality results such as Serre and Herzog-Rahimi dualities.

Contribution

It introduces a new duality theorem that encompasses multiple known dualities in the context of graded algebras over a field.

Findings

Unified duality framework for local cohomology and generalized local cohomology

Derivation of known dualities as special cases of the main theorem

Enhanced understanding of duality relations in graded algebra contexts

Abstract

We prove a duality theorem for graded algebras over a field that implies several known duality results : graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.