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Paper   IPM / M / 11792
School of Mathematics
  Title:   Cofiniteness of composed local cohomology modules
  Author(s):  A. Mafi
  Status:   To Appear
  Journal: Forum Math.
  Supported by:  IPM
Let R be a commutative Noetherian ring, \mathfraka ⊆ \mathfrak b be two ideals of R and M be a finitely generated R-module. We prove that H\mathfrak bj(H\mathfrak ai(M)) is \mathfrak b-cofinite for all i and j in the follwing cases: (1)dim R/\mathfrak b=0 and dim R/\mathfrak a=1,(2)dim R/\mathfrak b=1 and dim R/\mathfrak a=1.
In case (1),we also prove that H\mathfrakbj(H\mathfrak ai(M)) is Artinian for all i and j. Additionally, we show that if dim R/\mathfrak b=1 and dim R/\mathfrak a=2 and n is a non-negative integer such that H\mathfrakai(M) is finitely generated for all i < n, then H\mathfrakb0(H\mathfrak an(M)) is \mathfrak b-confinite.

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