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A Note on the Vanishing of Certain Local Cohomology Modules

Published online by Cambridge University Press:  20 November 2018

M. Hellus
M. Hellus*
Affiliation:
Fakultaet fuer Mathematik, Universitaet Regensburg, 93040 Regensburg, Germanye-mail: [email protected]
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Abstract

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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.

Keywords

13D45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012 , pp. 315 - 318
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Brodmann, M. P. and Sharp, R. J., Local Cohomology: An algebraic introduction with geometric applications. Cambridge Studies in Advanced Mathematics 60. Cambridge University Press, Cambridge, 1998.Google Scholar
[2] Hartshorne, R., Algebraic Geometry. Graduate Texts in Mathematics 52. Springer-Verlag, New York, 1977.Google Scholar