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Paper IPM / M / 466  


Abstract:  
Let A be a commutative Noetherian ring, let M be a finitely
generated Amodule, and let \frak a,\frak b be ideals of
A with \frakb ⊆ \fraka. In this paper, firstly, we
determine precisely the set of associated primes of the first
nonfinitely generated local cohomology module H^{n}_{\fraka}(M). Then we give an affirmative answer, in certain cases, to the
following question: If, for each prime ideal \frakp of A,
there exists an integer k(\frakp) such that
\frakb^{k(\frakp)} H^{i}_{\fraka A\frakp}(M_{\frakp})=0 for every i less than a fixed integer n,
then does there exist an integer k such that \frakb^{k}H^{i}_{\fraka} (M)=0 for all i < n. A formulation of this
question is referred as the generalized localglobal principle for
the finiteness of local cohomology modules.
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