On vanishing of generalized local cohomology modules

Details On vanishing of generalized local cohomology modules On vanishing of generalized local cohomology modules

2004-08-26

arxiv.org/abs/math/0408368v1

Mathematics

Commutative Algebra

7 pages, to appear in Algebra Colloquium

Scientific paper

Let $\fa$ denote an ideal of a $d$-dimensional Gorenstein local ring $R$ and
$M$ and $N$ two finitely generated $R$-modules with $\pd M< \infty$. It is
shown that $H^d_{\fa}(M,N)=0$ if and only if $\dim \hat{R}\big/
\fa\hat{R}+\fp>0$ for all
$\fp\in\Ass_{\hat{R}}\hat{M}\cap\Supp_{\hat{R}}\hat{N}$.

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