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A Note on the Vanishing of Certain Local Cohomology Modules
Published online by Cambridge University Press: 20 November 2018
Abstract
For a finite module $M$ over a local, equicharacteristic ring
$(R,\,m)$, we show that the well-known formula
$\text{cd(m,}\,M)\,=\,\dim\,M$ 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.
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- Copyright © Canadian Mathematical Society 2012