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| Paper IPM / M / 466 |
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| Abstract: | |||||
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Let A be a commutative Noetherian ring, let M be a finitely
generated A-module, 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
non-finitely generated local cohomology module Hn\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
\frakbk(\frakp) Hi\fraka A\frakp(M\frakp)=0 for every i less than a fixed integer n,
then does there exist an integer k such that \frakbkHi\fraka (M)=0 for all i < n. A formulation of this
question is referred as the generalized local-global principle for
the finiteness of local cohomology modules.
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