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Cofiniteness and vanishing of local cohomology modules

Published online by Cambridge University Press:  24 October 2008

Craig Huneke  and
Jee Koh
Craig Huneke
Affiliation:
Department of Mathematics, Purdue University, W. Lafayette, IN 47907, U.S.A.
Jee Koh
Affiliation:
Department of Mathematics, University of Indiana, Bloomington, IN 47405, U.S.A.
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Extract

Let R be a noetherian local ring with maximal ideal m and residue field k. If M is a finitely generated R-module then the local cohomology modules are known to be Artinian. Grothendieck [3], exposé 13, 1·2 made the following conjecture:

If I is an ideal of R and M is a finitely generated R-module, then HomR (R/I, ) is finitely generated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 421 - 429
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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