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Paper   IPM / M / 466
School of Mathematics
  Title:   On the local-global principle and the finiteness of associated primes of local cohomology modules
1.  R. Tajarod
2.  H. Zakeri
  Status:   Published
  Journal: Math. J. Toyama Univ.
  Vol.:  23
  Year:  2000
  Pages:   29-40
  Supported by:  IPM
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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