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arXiv · 0705.4553

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

Nguyen Tu Cuong·Nguyen Van Hoang
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Abstract

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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Nguyen Tu Cuong, Nguyen Van Hoang. 2007-05-31. On the Vanishing and the Finiteness of Supports of Generalized Local Cohomology Modules. https://arxiv.org/abs/0705.4553

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