Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-16T18:07:11.042Z Has data issue: false hasContentIssue false
  • English
  • Français

On the cofiniteness of local cohomology modules

Published online by Cambridge University Press:  24 October 2008

Donatella Delfino
Donatella Delfino
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Let (R,m) be a local, noetherian, d-dimensional ring and let M be a finitely generated R-module. Since the local cohomology modules are artinian, is finitely generated for all i and j (see [4], Remark 1*middot;3 and 2·1). Grothendieck[2] made the following conjecture: If I is an ideal of a noetherian ring R, thenis finitely generated for all j.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 79 - 84
Copyright
Copyright © Cambridge Philosophical Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Brodmann, M. and Huneke, C.. A quick proof of the Hartshorne–Lichtenbaum Vanishing Theorem (preprint).Google Scholar
[2]Grothendieck, A.. Cohomologie locale des faisceaux cohérents et théorèm.es de Lefschelz locaux et globaux. S. G. A. II. (North Holland, 1968).Google Scholar
[3]Hartshorne, R.. Affine duality and cofiniteness. Invent. Math. 9 (1970), 145–164.CrossRefGoogle Scholar
[4]Huneke, C. and Koh, J.. Cofiniteness and vanishing of local cohomology modules. Math. Proc. Cambridge Philos. Soc. 110 (1991), 421–429.Google Scholar
[5]Huneke, C. and Lyubeznik, G.. On the vanishing of local cohomology modules. Invent. Math. 102 (1990), 73–93.Google Scholar
[6]Lyubeznik, G.. Finiteness properties of local cohomology modules (an application of D-modules to commutative algebra) (preprint).Google Scholar
[7]Matsumura, H.. Commutative Algebra, 2nd edn. (Benjamin/Cummings, Reading, Ma., 1980).Google Scholar
[8]Milne, J. S., Etale Cohomology (Princeton University Press, 1980).CrossRefGoogle Scholar
[9]Rotman, J.. An Introduction to Homological Algebra (Academic Press, 1979).Google Scholar