What question did this study set out to answer?

To determine the cofinite nature of local cohomology modules under certain conditions in Noetherian rings.

June 14, 2026Open Access

On the Cofiniteness of Local Cohomology Modules

Key Points

To determine the cofinite nature of local cohomology modules under certain conditions in Noetherian rings.
Assumed an ideal in a commutative Noetherian ring and derived properties of local cohomology modules.
Analyzed the cofinite property for local cohomology modules across all finitely generated modules.
Demonstrated that local cohomology modules are cofinite for all finitely generated modules in the specified context.
Established that if certain modules are cofinite, then all local cohomology modules share this property for any integer index.

Abstract

Suppose that is an ideal of a given commutative Noetherian ring R such that the R-modules H¹_ (M) and H³_ (M) are -cofinite, for every finitely generated R-modules M. In this paper, it is shown that the R-modules Hⁱ_ (M) are -cofinite, for all finitely generated R-modules M and all integers i₀.

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