A Note on the Vanishing of Certain Local Cohomology Modules

Abstract

For a finite module M over a local, equicharacteristic ring (R, m), we show that the well-known formula cd(m, M) = dim M becomes trivial if ones uses Matlis duals of local cohomology modules together with spectral sequences. We also prove a new ring-theoretic vanishing criterion for local cohomology modules.