Results of Formal Local Cohomology Modules

Amir Mafi

Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 1

Résumé

Let $(R,\frak{m})$ be a commutative Noetherian local ring, $\frak{a}$ an ideal of $R$, and $M$ a finitely generated $R$-module. We show that for a non-negative integer $t$ the following cases are equivalent: The formal local cohomology modules $\underset{n}{\varprojlim}H_{\frak{m}}^i(M/{{\frak{a}}^nM})$ are Artinian for all $i$ $t$; $\frak{a}\subseteq$ Rad$($Ann$(\underset{n}{\varprojlim}H_{\frak{m}}^i(M/{{\frak{a}}^nM})))$ for all $i$ $t$. If one of the above cases holds, then $\underset{n}{\varprojlim}H_{\frak{m}}^t(M/{{\frak{a}}^nM})/{{\frak{a}}\underset{n}{\varprojlim}H_{\frak{m}}^t(M/{{\frak{a}}^nM})}$ is Artinian. Also, there are some results concerning finiteness properties of formal local cohomology modules.

Détail

Classification : 13D45, 13E99