A characterization result of cofinite local cohomology modules
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2023
- DOI:
- 10.48550/arXiv.2305.10202
- arXiv:
- arXiv:2305.10202
- Bibcode:
- 2023arXiv230510202A
- Keywords:
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- Mathematics - Commutative Algebra;
- 13D45;
- 13E05;
- 14B15
- E-Print:
- 12 pages