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.
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This work is supported in part by the National Basis Research Programme in Natural Science of Vietnam.
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Cuong, N.T., Van Hoang, N. On the vanishing and the finiteness of supports of generalized local cohomology modules. manuscripta math. 126, 59–72 (2008). https://doi.org/10.1007/s00229-007-0162-7
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DOI: https://doi.org/10.1007/s00229-007-0162-7