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Paper   IPM / M / 8289
School of Mathematics
  Title:   Artinianess of graded local cohomology modules
  Author(s):  R. Sazeedeh
  Status:   Published
  Journal: Proc. Amer. Math. Soc.
  Vol.:  135
  Year:  2007
  Pages:   2339–2345
  Supported by:  IPM
Let R = ⊕n ∈ \mathbbN0 Rn be a Noetherian homogeneous ring with local base ring (R0, \frakm0) and let M be a finitely generated graded R-module. Let a be the largest integer such that HaR+ (M) is not Artinian. We will prove that HiR+ (M)/\frakm0HiR+(M) are Artinian for all ia and there exists a polynomial ~P ∈ \mathbbQ[x] of degree less than a such that lengthR0HaR+(M)n/\frakm0HaR+((M)n)=~P(n) for all n << 0. Let s be the first integer such that the local cohomology module HsR+ (M) is not R+-cofinite. We will show that for all is the graded module Γ\frakm0(HiR+ (M)) are Artinian.

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