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Paper   IPM / M / 8785
School of Mathematics
  Title:   Cofinite modules and generalized local cohomology
  Author(s):  A. Mafi (Joint with H. Saremi)
  Status:   Published
  Journal: Houston J. Math.
  Vol.:  35
  Year:  2009
  Pages:   1013-1018
  Supported by:  IPM
Let R be a commutative Noetherian ring, \fraka an ideal of R, and M, N two finitely generated R-modules. We prove that the generalized local cohomology modules Ht\fraka(M,N) are \fraka-cofinite; that is, ExtiR(R/\fraka,Ht\fraka(M, N) is finitely generated for all i, t ≥ 0, in the following

    (i) cd(\fraka) = 1, where cd is the cohomological dimension of \fraka in R.
    (ii) dimR ≤ 2.
Additionally, we show that if cd(\fraka) = 1 then ExtiR(M, Ht\fraka(N)) is \fraka-cofinite for all i, t ≥ 0.

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