Finiteness properties for matlis reflexive modules

Abstract

The local cohomology modules H^J _I(M) of a Matlis reflexive module are shown to be I-cofinite when j >= 1 and have finite Bass numbers when j >= 0, where I is an ideal satisfying any one of a list of properties. In addition, we show that the completion of a Matlis reflexive module is finitely generated over the completion of the ring and we classify Matlis reflexive modules over a one dimensional ring.

Keywords:

• Matlis reflexive module
• local cohomology
• Gorenstein ring
• Bass numbers