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• W2085346022 endingPage "2011" @default.
• W2085346022 startingPage "1997" @default.
• W2085346022 abstract "Let R be a commutative Noetherian ring and let M be a non-zero finitely generated R-module. Let I be an ideal of R and t a non-negative integer such that dimSuppHIi(M)⩽1 for all i<t. It is shown that the R-modules HI0(M),HI1(M),…,HIt−1(M) are I-cofinite and the R-module HomR(R/I,HIt(M)) is finitely generated. This immediately implies that if I has dimension one (i.e., dimR/I=1), then HIi(M) is I-cofinite for all i⩾0. This is a generalization of the main results of Delfino and Marley [D. Delfino, T. Marley, Cofinite modules and local cohomology, J. Pure Appl. Algebra 121 (1997) 45–52] and Yoshida [K.I. Yoshida, Cofiniteness of local cohomology modules for ideals of dimension one, Nagoya Math. J. 147 (1997) 179–191] for an arbitrary Noetherian ring R. Also, we prove that if R is local and dimSuppHIi(M)⩽2 for all i<t, then the R-modules ExtRj(R/I,HIi(M)) and HomR(R/I,HIt(M)) are weakly Laskerian for all i<t and all j⩾0. As a consequence, it follows that the set of associated primes of HIi(M) is finite for all i⩾0, whenever dimR/I⩽2." @default.
• W2085346022 created "2016-06-24" @default.
• W2085346022 creator A5032279395 @default.
• W2085346022 creator A5079917554 @default.
• W2085346022 date "2009-04-01" @default.
• W2085346022 modified "2023-10-12" @default.
• W2085346022 title "Cofiniteness of local cohomology modules for ideals of small dimension" @default.
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• W2085346022 doi "https://doi.org/10.1016/j.jalgebra.2008.12.020" @default.
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