SOCLE FINITENESS OF THE LOCAL COHOMOLOGY

Let R be a Gorenstein local ring and I an ideal of R. Denote by H(I, R) the assertion: "The socle of the local cohomology module H-I(n)(R) is finitely generated for each n >= 0." We translate H(I, R) into a property of the minimal injective coresolution of R, and then use this translation to prove H(I, R) for all regular local rings R and all ideals I with level prime avoidance.