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Paper IPM / M / 8289  


Abstract:  
Let R = ⊕_{n ∈ \mathbbN0} R_{n} be a Noetherian
homogeneous ring with local base ring (R_{0}, \frakm_{0}) and
let M be a finitely generated graded Rmodule. Let a be the
largest integer such that H^{a}_{R+} (M) is not Artinian. We
will prove that H^{i}_{R+} (M)/\frakm_{0}H^{i}_{R+}(M)
are Artinian for all i ≥ a and there exists a polynomial
~P ∈ \mathbbQ[x] of degree less than a such that
length_{R0}H^{a}_{R+}(M)_{n}/\frakm_{0}H^{a}_{R+}((M)_{n})=~P(n) for all
n << 0. Let s be the first integer such that the local
cohomology module
H^{s}_{R+} (M) is not R_{+}cofinite. We will show that for all i ≤ s the
graded module Γ_{\frakm0}(H^{i}_{R+} (M)) are
Artinian.
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