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Cofiniteness of local cohomology modules and subcategories of modules

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Abstract

Let R be a commutative noetherian ring and I an ideal of R. Assume that for all integers i the local cohomology module \({\text {H}}_I^i(R)\) is I-cofinite. Suppose that \(R_\mathfrak {p}\) is a regular local ring for all prime ideals \(\mathfrak {p}\) that do not contain I. In this paper, we prove that if the I-cofinite modules form an abelian category, then for all finitely generated R-modules M and all integers i, the local cohomology module \({\text {H}}_I^i(M)\) is I-cofinite.

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Acknowledgements

The authors thank Kamal Bahmanpour, Ken-ichiroh Kawasaki and Takeshi Yoshizawa for valuable, useful and helpful comments.

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  1. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

    Ryo Takahashi & Naoki Wakasugi

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  1. Ryo Takahashi
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  2. Naoki Wakasugi
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Correspondence to Naoki Wakasugi.

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RT was partly supported by JSPS Grant-in-Aid for Scientific Research 19K03443 and 23K03070.

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Takahashi, R., Wakasugi, N. Cofiniteness of local cohomology modules and subcategories of modules. Collect. Math. (2023). https://doi.org/10.1007/s13348-023-00416-6

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