Finiteness Properties of Duals of Local Cohomology Modules

Abstract

We investigate Matlis duals of local cohomology modules and prove that, in general, their zeroth Bass number with respect to the zero ideal is not finite. We also prove that, somewhat surprisingly, if we apply local cohomology again (i.e., to the Matlis dual of the local cohomology module), we get (under certain hypotheses) either zero or E, an R-injective hull of the residue field of the local ring R.

Key Words:

• Bass numbers
• Local cohomology
• Matlis duality

2000 Mathematics Subject Classification:

• 13D45
• 13C05

ACKNOWLEDGMENT

The author thanks Gennady Lyubeznik for helpful discussions, in particular on D-modules.

Notes

Communicated by W. Bruns.