The Artinianness of Formal Local Cohomology Modules

Yan Gu

Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 2

Résumé

Let I be an ideal of a commutative Noetherian local ring $(R,\frak{m})$, $M$ a finitely generated $R$-module and $\underset{n}{\varprojlim}\, H^i_{\frak{m}}(M/I^nM)$ the $i$-th formal local cohomology module of $M$ with respect to $I$. We prove some results concerning artinianness of $\underset{n}{\varprojlim}\,H^i_{\frak{m}}(M/I^nM)$. We discuss the maximum and minimum integers such that $\underset{n}{\varprojlim}\, H^i_{\frak{m}}(M/I^nM)$ is artinian.

Détail

Classification : 13D45, 13E10, 13E15