GENERALIZED LOCAL COHOMOLOGY AND THE INTERSECTION THEOREM

ABSTRACT

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 RΓ_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  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.

Key Words:

• Cohomological dimension
• Complexes of modules
• Intersection theorem

Mathematics Subject Classification:

• 13D45
• 13D22
• 13D25
• 13D05

ACKNOWLEDGMENTS

The authors would like to thank the referee for his or her substantial comments. The research of the first author was supported by a grant from the IPM (No. 82130014). The second author was supported by a grant from the University of Tehran (No. 511/3/702).

Notes

^#Communicated by I. Swanson.