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A lifting result for local cohomology of graded modules

  • M. Brodmann


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.



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(1)Brodmann, M.Finiteness of ideal transforms. J. Alg. 63 (1980), 162185.
(2)Brodmann, M.Kohomologische Eigenschaften von Aufblasungen an lokal vollständigen Durchschnitten, Habilitationsschrift Münster, 1980.
(3)Fossum, R. and Foxby, H.-B.The category of graded modules. Math. Scand. 35 (1974), 288300.
(4)Grothendieck, A.EGA IV, Publ. Math. I.H.E.S. 24 (1965).
(5)Grothendieck, A.SGA II (North Holland, Amsterdam, 1968).
(6)Hartshorne, R.Algebraic geometry (Springer, 1977).
(7)Serre, J. P. Fac.Annals of Math. 61, no. 2 1955), 197278.
(8)Matsumura, H.Commutative algebra (Benjamin 1970).
(9)Nguen Tu, Chuong, Ngo Viet, Trung and Schenzel, P.Verallgemeinerte Cohen-Maculay-Moduln. Math. Nachr. 85 (1978), 5775.

A lifting result for local cohomology of graded modules

  • M. Brodmann


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