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manuscripta mathematica

, Volume 126, Issue 1, pp 59–72 | Cite as

On the vanishing and the finiteness of supports of generalized local cohomology modules

  • Nguyen Tu CuongEmail author
  • Nguyen Van Hoang
Article

Abstract

Let \((R, {\mathfrak{m}})\) be a Noetherian local ring, I an ideal of R and M, N two finitely generated R-modules. The first result of this paper is to prove a vanishing theorem for generalized local cohomology modules which says that \(H^j_I(M, N) = 0\) for all j > dim(R), provided M is of finite projective dimension. Next, we study and give characterizations for the least and the last integer r such that Supp\((H^r_I(M, N))\) is infinite.

Mathematics Subject Classification (2000)

13D45 13C15 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam

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