Geodesic
Cominimaxness of local cohomology modules
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 75-86 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$. Let $t\in \mathbb {N}_0$ be an integer and $M$ an $R$-module such that ${\rm Ext}^i_R(R/I,M)$ is minimax for all $i\leq t+1$. We prove that if $H^{i}_{I}(M)$ is ${\rm FD}_{\leq 1}$ (or weakly Laskerian) for all $i$, then the $R$-modules $H^{i}_{I}(M)$ are $I$-cominimax for all $i$ and ${\rm Ext}^i_R(R/I,H^{t}_{I}(M))$ is minimax for $i=0,1$. Let $N$ be a finitely generated $R$-module. We prove that ${\rm Ext}^j_R(N,H^{i}_{I}(M))$ and ${\rm Tor}^R_{j}(N,H^{i}_I(M))$ are $I$-cominimax for all $i$ and $j$ whenever $M$ is minimax and $H^{i}_{I}(M)$ is ${\rm FD}_{\leq 1}$ (or weakly Laskerian) for all $i$.
Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$. Let $t\in \mathbb {N}_0$ be an integer and $M$ an $R$-module such that ${\rm Ext}^i_R(R/I,M)$ is minimax for all $i\leq t+1$. We prove that if $H^{i}_{I}(M)$ is ${\rm FD}_{\leq 1}$ (or weakly Laskerian) for all $i$, then the $R$-modules $H^{i}_{I}(M)$ are $I$-cominimax for all $i$ and ${\rm Ext}^i_R(R/I,H^{t}_{I}(M))$ is minimax for $i=0,1$. Let $N$ be a finitely generated $R$-module. We prove that ${\rm Ext}^j_R(N,H^{i}_{I}(M))$ and ${\rm Tor}^R_{j}(N,H^{i}_I(M))$ are $I$-cominimax for all $i$ and $j$ whenever $M$ is minimax and $H^{i}_{I}(M)$ is ${\rm FD}_{\leq 1}$ (or weakly Laskerian) for all $i$.
DOI : 10.21136/CMJ.2018.0161-17
Classification : 13C05, 13D45, 13E10
Keywords: local cohomology; ${\rm FD}_{\leq n}$ modules; cofinite modules; cominimax modules 
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     author = {Aghapournahr, Moharram},
     title = {Cominimaxness of local cohomology modules},
     journal = {Czechoslovak Mathematical Journal},
     pages = {75--86},
     year = {2019},
     volume = {69},
     number = {1},
     doi = {10.21136/CMJ.2018.0161-17},
     mrnumber = {3923575},
     zbl = {07088770},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0161-17/}
}
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Aghapournahr, Moharram. Cominimaxness of local cohomology modules. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 75-86. doi: 10.21136/CMJ.2018.0161-17

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