On the asymptotic behaviour of associated primes of generalized local cohomology modules

Abstract

Let M and A' be finitely generated and graded modules over a standard positive graded commutative Noetherian ring R, with irrelevant ideal /?+. Let H# (M, N) n be the nth component of the graded generalized local cohomology module H R+ (M, N). In this paper we study the asymptotic behavior of Assfl + (//| + (Af, N) n ) as n ->• -oo whenever k is the least integer j for which the ordinary local cohomology module H' R+ (N) is not finitely generated.