FINITELY GRADED LOCAL COHOMOLOGY AND THE DEPTHS OF GRADED ALGEBRAS

The term ''finitely graded'' is introduced here to refer to graded mod ules which are nonzero in only finitely many graded pieces. We conside r the question of when the local cohomology modules of a graded module are finitely graded. Using a theorem of Faltings concerning the annih ilation of local cohomology, we obtain some partial answers to this qu estion. These results are then used to compare the depths of the Pees algebra and the associated graded ring of an ideal in a local ring.