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Symbolic powers and local cohomology

Part of: Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  26 February 2010

Jaume Martí-Farré
Jaume Martí-Farré
Affiliation:
Dept. Matemàtica Aplicada i Telemàtica, ETSETB, Universitat Politècnica de Catalunya, C/Gran Capità s/n, Mòdul C3, Campus Nord, 08034-Barcelona, Spain.
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Abstract

Let I be an ideal of a Noetherian ring R. The purpose of this paper is to study the relationship between the vanishing of the local cohomology modules , and the comparison of the topologies defined by the I-adic {In}n≥0, the symbolic {I(n)}n≥0 and the integral filtration

MSC classification

Secondary: 16P40: Noetherian rings and modules
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 182 - 187
Copyright
Copyright © University College London 1995

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References

1. Call, F. W.. On local cohomology modules. J. Pure Appl. Algebra, 43 (1986), 111–117.CrossRefGoogle Scholar
2. Call, F. W. and Sharp, R. Y.. A short proof of the local Lichtenbaum-Hartshorne theorem on the vanishing of local cohomology. Bull. London Math. Soc, 18 (1986), 261–264.CrossRefGoogle Scholar
3. Grothendieck, A.. Local cohomology (Springer-Verlag L.N.M. 41, 1967).Google Scholar
4. Hartshorne, R.. Cohomological dimension of algebraic varieties. Ann. of Math., 88 (1968), 403–450.CrossRefGoogle Scholar
5. McAdam, S.. Asymptotic Prime Divisors. (Springer-Verlag L.N.M. 1023, 1983).CrossRefGoogle Scholar
6. McAdam, S.. Quintasymptotic primes and four results of Schenzel. J. Pure Appl. Algebra, 47 (1987), 283–298.CrossRefGoogle Scholar
7. Peskine, C. and Szpiro, L.. Dimension projective finie et cohomologie locale. Publ. Math. I.H.E.S., 42 (1973), 77–119.CrossRefGoogle Scholar
8. Schenzel, P.. Explicit computations around the Lichtenbaum-Hartshorne vanishing theorem. Manuscripta Math., 78 (1993), 57–68.CrossRefGoogle Scholar
9. Sharp, R. Y.. On the attached prime ideals of certain artinian local cohomology modules. Proc. Edinburgh Math. Soc, 24 (1981), 9–14.CrossRefGoogle Scholar