A characterization result of cofinite local cohomology modules

Moharram Aghapournahr; Leif Melkersson

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arXiv · 2305.10202

A characterization result of cofinite local cohomology modules

Moharram Aghapournahr·Leif Melkersson

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Abstract

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, $M$ an arbitrary $R$-module and $N$ a finite $R$-module. We prove that \cite[Theorem 2.1]{Mel} and \cite[Proposition 3.3 (i)$\Leftrightarrow$(ii)]{B1} are true for any Serre subcategory of $R$-modules. We also prove a characterization theorem for $\lc_{\fa}^{i}(M)$ and $\lc_{\fa}^{i}(N,M)$ to be $\fa$-cofinite for all $i$, whenever one of the following cases holds: (a) $\ara (\fa)\leq 1$, (b) $\dim R/\fa \leq 1$ or (c) $\dim R\leq 2$. In the end we study Artinianness and Artinian $\fa$-cofiniteness of local cohomology modules.

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Moharram Aghapournahr, Leif Melkersson. 2023-05-17. A characterization result of cofinite local cohomology modules. https://arxiv.org/abs/2305.10202

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