“School of Mathematics”
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| Paper IPM / M / 8289 |
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| Abstract: | |
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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 i ≥ a 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 i ≤ s the
graded module Γ\frakm0(HiR+ (M)) are
Artinian.
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