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# A Note on the Vanishing of Certain Local Cohomology Modules

Published:2011-03-25
Printed: Jun 2012
• M. Hellus,
Fakultaet fuer Mathematik, Universitaet Regensburg, 93040 Regensburg, Germany
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## Abstract

For a finite module $M$ over a local, equicharacteristic ring $(R,m)$, we show that the well-known formula $\textrm{cd}(m,M)=\dim M$ 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.