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november 2020 Cofiniteness properties of generalized local cohomology modules
Moharram Aghapournahr, Mahmoud Behrouzian
Bull. Belg. Math. Soc. Simon Stevin 27(4): 521-533 (november 2020). DOI: 10.36045/j.bbms.190810

Abstract

Let $R$ be a commutative Noetherian ring and $I$ an ideal of $R$. Let $t\in\Bbb{N}_0$ be an integer, $M$ a finitely generated $R$-module and $X$ be an $R$-module such that $\Ext^i_R(R/I,X)$ is finitely generated (resp. minimax, weakly Laskerian) for all $i\leq t+1$. We prove that if $H^{i}_{I}(M, X)$ is ${\rm FD_{\leq 1}}$ for all $i<t$, then the $R$-modules $H^{i}_{I}(M,X)$ are $I$-cofinite (resp. $I$-cominimax, $I$-weakly cofinite) for all $i<t$ and for any ${\rm FD_{\leq 0}}$ (or minimax) submodule $N$ of $H^{t}_{I}(M,X)$, the $R$-module $\Ext^i_R(R/I,H^{t}_{I}(M,X)/N)$ is finitely generated (resp. minimax, weakly Laskerian) for $i=0,1$. In particular the set $Ass_R(H^{t}_{I}(M,X)/N)$ is a finite set.

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Moharram Aghapournahr. Mahmoud Behrouzian. "Cofiniteness properties of generalized local cohomology modules." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 521 - 533, november 2020. https://doi.org/10.36045/j.bbms.190810

Information

Published: november 2020
First available in Project Euclid: 20 November 2020

MathSciNet: MR4177391
Digital Object Identifier: 10.36045/j.bbms.190810

Subjects:
Primary: 13D45, 13E05, 14B15

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 4 • november 2020
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