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COFINITENESS OF LOCAL COHOMOLOGY MODULES OVER REGULAR LOCAL RINGS

Published online by Cambridge University Press:  01 January 2000

GABRIEL CHIRIACESCU
GABRIEL CHIRIACESCU
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania
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Abstract

It is well known that for a Noetherian ring R, an ideal I of R, and M a finitely generated R-module, the local cohomology modules HiI(M) are not always finitely generated. On the other hand, if R is local and m is its maximal ideal, then Him(M) are Artinian modules, which is equivalent to the following two properties:

(i) SuppR(Him(M)) ⊆{m};

(ii) the vector space HomR(k, Him(M)) has finite dimension over k, where k = R/m.

Taking these facts into account, Grothendieck [9] made the following conjecture.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 1 , January 2000 , pp. 1 - 7
Copyright
© The London Mathematical Society 2000

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