Some results on the cofiniteness of local cohomology modules
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 105-110.
Voir la notice de l'article dans Czech Digital Mathematics Library
Let $R$ be a commutative Noetherian ring, $\mathfrak {a}$ an ideal of $R$, $M$ an $R$-module and $t$ a non-negative integer. In this paper we show that the class of minimax modules includes the class of $\mathcal {AF}$ modules. The main result is that if the $R$-module ${\rm Ext}^t_R(R/\mathfrak {a},M)$ is finite (finitely generated), $H^i_\mathfrak {a}(M)$ is $\mathfrak {a} $-cofinite for all $i$ and $H^t_\mathfrak {a}(M)$ is minimax then $H^t_\mathfrak {a}(M)$ is $\mathfrak {a} $-cofinite. As a consequence we show that if $M$ and $N$ are finite $R$-modules and $H^i_\mathfrak {a}(N)$ is minimax for all $i$ then the set of associated prime ideals of the generalized local cohomology module $H^t_\mathfrak {a}(M,N)$ is finite.
DOI :
10.1007/s10587-012-0019-4
Classification :
13D45, 13E05, 14B15
Mots-clés : local cohomology; cofinite modules; mimimax modules; AF modules; associated primes
Mots-clés : local cohomology; cofinite modules; mimimax modules; AF modules; associated primes
@article{10_1007_s10587_012_0019_4, author = {Laleh, Sohrab Sohrabi and Sadeghi, Mir Yousef and Mostaghim, Mahdi Hanifi}, title = {Some results on the cofiniteness of local cohomology modules}, journal = {Czechoslovak Mathematical Journal}, pages = {105--110}, publisher = {mathdoc}, volume = {62}, number = {1}, year = {2012}, doi = {10.1007/s10587-012-0019-4}, mrnumber = {2899737}, zbl = {1249.13012}, language = {en}, url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0019-4/} }
TY - JOUR AU - Laleh, Sohrab Sohrabi AU - Sadeghi, Mir Yousef AU - Mostaghim, Mahdi Hanifi TI - Some results on the cofiniteness of local cohomology modules JO - Czechoslovak Mathematical Journal PY - 2012 SP - 105 EP - 110 VL - 62 IS - 1 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0019-4/ DO - 10.1007/s10587-012-0019-4 LA - en ID - 10_1007_s10587_012_0019_4 ER -
%0 Journal Article %A Laleh, Sohrab Sohrabi %A Sadeghi, Mir Yousef %A Mostaghim, Mahdi Hanifi %T Some results on the cofiniteness of local cohomology modules %J Czechoslovak Mathematical Journal %D 2012 %P 105-110 %V 62 %N 1 %I mathdoc %U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0019-4/ %R 10.1007/s10587-012-0019-4 %G en %F 10_1007_s10587_012_0019_4
Laleh, Sohrab Sohrabi; Sadeghi, Mir Yousef; Mostaghim, Mahdi Hanifi. Some results on the cofiniteness of local cohomology modules. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 105-110. doi : 10.1007/s10587-012-0019-4. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0019-4/
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