On vanishing of generalized local cohomology modules
Abstract
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 $\fp\in\Ass_{\hat{R}}\hat{M}\cap\Supp_{\hat{R}}\hat{N}$.