On the Vanishing and the Finiteness of Supports of Generalized Local Cohomology Modules

Details On the Vanishing and the Finiteness of Supports of Generalized Local Cohomology Modules On the Vanishing and the Finiteness of Supports of Generalized Local Cohomology Modules

2007-05-31

arxiv.org/abs/0705.4553v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

Let $(R,\fr m)$ be a Noetherian local ring, $I$ an ideal of $R$ and $M, N$ two finitely generated $R$-modules. The first result of this paper is to prove a vanishing theorem for generalized local cohomology modules which says that $H^j_I(M,N)=0$ for all $j>\dim(R)$, provided $M$ is of finite projective dimension. Next, we study and give characterizations for the least and the last integer $r$ such that $\Supp(H^r_I(M,N))$ is infinite.

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