Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-25T14:00:25.938Z Has data issue: false hasContentIssue false
  • English
  • Français

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: michael.hellus@mathematik.uni-regensburg.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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