Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-06T18:47:44.880Z Has data issue: false hasContentIssue false
  • English
  • Français

On the attached prime ideals of certain Artinian local cohomology modules

Published online by Cambridge University Press:  20 January 2009

R. Y. Sharp
R. Y. Sharp
Affiliation:
Department of Pure MathematicsUniversity of SheffieldSheffield S3 7RH
Rights & Permissions [Opens in a new window]

Extract

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.

The study of the cohomological dimensions of algebraic varieties has produced some interesting results and problems in local algebra: the general local problem is that posed by Hartshorne and Speiser in (4, p. 57). We consider a (commutative, Noetherian) local ring A (with identity), a proper ideal a of A, and ask the following question.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 9 - 14
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Bass, H., On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8–28.Google Scholar
(2)Grothendieck, A., Local cohomology (Lecture notes in mathematics No. 41, Berlin-Heidelberg-New York, Springer, 1967).Google Scholar
(3)Hartshorne, R., Cohomological dimension of algebraic varieties, Annals of Math. 88 (1968), 403–450.Google Scholar
(4)Hartshorne, R. and Speiser, R., Local cohomological dimension in characteristic p, Annals of Math. 105 (1977), 45–79.Google Scholar
(5)Kirby, D., Coprimary decomposition of Artinian modules, J. London Math. Soc. 6 (1973), 571–576.Google Scholar
(6)Macdonald, I. G. and Sharp, R. Y., An elementary proof of the non-vanishing of certain local cohomology modules, Quart. J. Math. Oxford (2) 23 (1972), 197–204.Google Scholar
(7)Macdonald, I. G., Secondary representation of modules over a commutative ring, Symposia Mathematica 11 (1973), 23–43.Google Scholar
(8)Matlis, E., Injective modules over Noetherian rings, Pacific J. Math. 8 (1958), 511–528.Google Scholar
(9)Northcott, D. G., Generalized Koszul complexes and Artinian modules, Quart. J. Math. Oxford (2) 23 (1972), 289–297.Google Scholar
(10)Ogus, A., Local cohomological dimension of algebraic varieties, Annals of Math. 98 (1973), 327–365.Google Scholar
(11)Peskine, C. and Szpiro, L., Dimension projective finie et cohomologie locale, Inst. Haut. Étud. Sci., Publ. Math. 42 (1973), 323–395.Google Scholar
(12)Sharp, R. Y., Local cohomology theory in commutative algebra, Quart. J. Math. Oxford (2) 21 (1970), 425–434.Google Scholar
(13)Sharp, R. Y., Some results on the vanishing of local cohomology modules, Proc. London Math. Soc. (3) 30 (1975), 177–195.Google Scholar
(14)Sharp, R. Y., Secondary representations for injective modules over commutative Noetherian rings, Proc. Edinburgh Math. Soc. (2) 20 (1976), 143–151.Google Scholar
(15)Sharpe, D. W. and Vámos, P., Injective modules (Cambridge tracts in mathematics and mathematical physics No. 62, Cambridge University Press, 1972).Google Scholar