UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let R be a commutative Noetherian ring with non-zero identity and a an ideal of R. Let M be a finite R-module of finite projective dimension and N an arbitrary finite R-module. We characterize the membership of the generalized local cohomology modules Hi a(M;N) in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let S be a Serre subcategory of the category of R{modules and n pdM be an integer such that Hi a(M;N) belongs to S for all i n.