Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T22:26:35.986Z Has data issue: false hasContentIssue false
  • English
  • Français

A lifting result for local cohomology of graded modules

Published online by Cambridge University Press:  24 October 2008

M. Brodmann
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we prove a lifting result for local cohomology. As a special case we get the following result for the Serre-cohomology over a projective variety:

Proposition (1·1). Let ℱ be a coherent sheaf over X, where X is a projective variety over an algebraically closed field k. Let i ≽ 0 and assume that there is a pencil P of hyper-plane sections which is in general position with respect to ℱ (which means that x ∉ H, ∀x ∈ Ass(ℱ), ∀H∈p), and such that for each H ∈ P Hi(X, ℱ│H(n)) = 0, ∀n ≪ 0. Then Hi + 1(X, ℱ) = 0, ∀n ≪ 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 2 , September 1982 , pp. 221 - 229
Copyright
Copyright © Cambridge Philosophical Society 1982

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.Finiteness of ideal transforms. J. Alg. 63 (1980), 162–185.CrossRefGoogle Scholar
(2)Brodmann, M.Kohomologische Eigenschaften von Aufblasungen an lokal vollständigen Durchschnitten, Habilitationsschrift Münster, 1980.Google Scholar
(3)Fossum, R. and Foxby, H.-B.The category of graded modules. Math. Scand. 35 (1974), 288–300.CrossRefGoogle Scholar
(4)Grothendieck, A.EGA IV, Publ. Math. I.H.E.S. 24 (1965).Google Scholar
(5)Grothendieck, A.SGA II (North Holland, Amsterdam, 1968).Google Scholar
(6)Hartshorne, R.Algebraic geometry (Springer, 1977).CrossRefGoogle Scholar
(7)Serre, J. P. Fac.Annals of Math. 61, no. 2 1955), 197–278.CrossRefGoogle Scholar
(8)Matsumura, H.Commutative algebra (Benjamin 1970).Google Scholar
(9)Nguen Tu, Chuong, Ngo Viet, Trung and Schenzel, P.Verallgemeinerte Cohen-Maculay-Moduln. Math. Nachr. 85 (1978), 57–75.Google Scholar