Let $R$ be commutative Noetherian ring and let $\fa$ be an ideal of $R$. For complexes $X$ and $Y$ of $R$--modules we investigate the invariant $\inf{ \mathbf R}\Gamma_{ \fa}({ \mathbf R}\Hom_R(X,Y))$ in certain cases. It is shown that, for bounded complexes $X$ and $Y$ with finite homology, $\dim Y\le\dim{ \mathbf R}\Hom_R(X,Y)\le\pd X+\dim(X\otimes^{ \mathbf L}_RY)+\sup X$ which strengthen the Intersection Theorem. Here $\inf X$ and $\sup X$ denote the homological infimum, and supremum of the complex $X$, respectively.
Categories: math.AC