Socle finiteness of the local cohomology
Let \(R\) be a commutative local noetherian ring. Finiteness properties of local cohomology modules over \(R\) are among the basic topics of local cohomology theory. One of the main question is as follows ``Let \(I\) be an ideal of \(R\). Is the socle of \(H^n_I(R)\) finitely generated?'' A positive answer to this question for all regular local ring was conjectured by Huneke. In the paper under review the authors proved the following result: Theorem. Let \(R\) be a regular local ring, and let \(I\) be an ideal with level prime avoidance. Then the socle of \(H^n_I(R)\) is finitely generated.
scientific article; zbMATH DE number 5858892
scientific article