An application of Serre-Grothendieck duality theorem to local cohomology

On Reducing sequences and an Application to Local Cohomology Modules

A Duality Theorem for Generalized Local Cohomology

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.

Extension functors of generalized local cohomology modules and Serre subcategories

In this paper we present several results concerning the cofiniteness of generalized local cohomology modules.

Serre Subcategories and Local Cohomology Modules with Respect to a Pair of Ideals

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

The Riemann-roch Theorem and Serre Duality

We introduce sheaves and sheaf cohomology and use them to prove the Riemann-Roch theorem and Serre duality. The main proofs follow the treatment in Forster [3].