Local Cohomology and Gorenstein Injective Dimension over Local Homomorphisms
نویسندگان
چکیده
Let φ : (R, m)→ (S, n) be a local homomorphism of commutative noetherian local rings. Suppose that M is a finitely generated S-module. A generalization of Grothendieck’s non-vanishing theorem is proved for M (i.e. the Krull dimension of M over R is the greatest integer i for which the ith local cohomology module of M with respect to m, Hi m(M), is non-zero). It is also proved that the Gorenstein injective dimension of M , if finite, is bounded below by dimension of M over R and is equal to the supremum of depthRp, where p runs over the support of M as an R-module.
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