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April 2015 On the cofiniteness of generalized local cohomology modules
Nguyen Tu Cuong, Shiro Goto, Nguyen Van Hoang
Kyoto J. Math. 55(1): 169-185 (April 2015). DOI: 10.1215/21562261-2848151

Abstract

Let R be a commutative Noetherian ring, let I be an ideal of R, and let M, N be two finitely generated R-modules. The aim of this paper is to investigate the I-cofiniteness of generalized local cohomology modules HIj(M,N)=limnExtRj(M/InM,N) of M and N with respect to I. We first prove that if I is a principal ideal, then HIj(M,N) is I-cofinite for all M, N and all j. Secondly, let t be a nonnegative integer such that dimSupp(HIj(M,N))1 for all j<t. Then HIj(M,N) is I-cofinite for all j<t and Hom(R/I,HIt(M,N)) is finitely generated. Finally, we show that if dim(M)2 or dim(N)2, then HIj(M,N) is I-cofinite for all j.

Citation

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Nguyen Tu Cuong. Shiro Goto. Nguyen Van Hoang. "On the cofiniteness of generalized local cohomology modules." Kyoto J. Math. 55 (1) 169 - 185, April 2015. https://doi.org/10.1215/21562261-2848151

Information

Published: April 2015
First available in Project Euclid: 13 March 2015

zbMATH: 1316.13024
MathSciNet: MR3323531
Digital Object Identifier: 10.1215/21562261-2848151

Subjects:
Primary: 13D45, 13E99, 18G60

Rights: Copyright © 2015 Kyoto University

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Vol.55 • No. 1 • April 2015
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