Some results on local cohomology modules

dc.creatorMafi, Amir
dc.date2005-12-03
dc.date.accessioned2026-07-07T06:54:49Z
dc.date.available2026-07-07T06:54:49Z
dc.descriptionLet $R$ 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.description7pages, Archiv der Mathematik
dc.identifierhttps://arxiv.org/abs/math/0512075
dc.identifierhttp://arxiv.org/abs/math/0512075
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106077
dc.subjectCommutative Algebra
dc.subject13D45
dc.titleSome results on local cohomology modules
dc.typetext

Files

Collections