Some results on local cohomology modules
| dc.creator | Mafi, Amir | |
| dc.date | 2005-12-03 | |
| dc.date.accessioned | 2026-07-07T06:54:49Z | |
| dc.date.available | 2026-07-07T06:54:49Z | |
| dc.description | Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, and let $M$ be a finitely generated $R$-module. For a non-negative integer $t$, we prove that $H_{\fa}^t(M)$ is $\fa$-cofinite whenever $H_{\fa}^t(M)$ is Artinian and $H_{\fa}^i(M)$ is $\fa$-cofinite for all $i<t$. This result, in particular, characterizes the $\fa$-cofiniteness property of local cohomology modules of certain regular local rings. Also, we show that for a local ring $(R,\fm)$, $f-\depth(\fa,M)$ is the least integer $i$ such that $H_{\fa}^i(M)\ncong H_{\fm}^i(M)$. This result in conjunction with the first one, yields some interesting consequences. Finally, we extend the non- vanishing Grothendieck's Theorem to $\fa$-cofinite modules. | |
| dc.description | 7pages, Archiv der Mathematik | |
| dc.identifier | https://arxiv.org/abs/math/0512075 | |
| dc.identifier | http://arxiv.org/abs/math/0512075 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106077 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D45 | |
| dc.title | Some results on local cohomology modules | |
| dc.type | text |