Generalized local cohomology and the intersection theorem

摘要

Let R be a commutative Noetherian ring and let a be an ideal of R. For complexes X and Y of R-modules we investigate the invariant inf R Gamma(a) (RHom(R) (X, Y)) in certain cases. It is shown that, for bounded complexes X and Y with finite homology, dim Y <= dim RHom(R) (X, Y) <= proj dim X + dim(X circle times(R)(L) Y) + sup X, which strengthen the intersection theorem. Here inf X and sup X denote the homological infimum and supremum of the complex X, respectively.