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Paper   IPM / M / 7710
School of Mathematics
  Title:   Associated primes of graded components of generalized local cohomology modules
  Author(s):  K. Khashyarmanesh
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  33
  Year:  2005
  Pages:   3081 – 3090
  Supported by:  IPM
We show that the i-th generalized local cohomology module of finitely generated graded modules M and N over a standard positive graded commutative Noetherian ring R, with respect to the irrelevant ideal R+, is itself graded; all its graded components are finitely generated modules over R0, the component of R of degree 0. Also we prove that the n-th component of HiR+(M,N)n of this generalized local cohomology module HiR+(M,N) is zero for all n >> 0. Moreover, in this paper, we study the asymptotic behaviour of AssR0(HiR+(M,N)n) as n→ −∞ in the following cases:
(i)]i is the least integer j for which HjR+(M,N) is not finitely generated.
(j)] The base ring R0 is local of dimension at most one and for all i ≥ 0.

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