On the vanishing, artinianness and finiteness of local cohomology modules

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dc.creatorAghapournahr, Moharram
dc.creatorMelkersson, Leif
dc.date2009-03-12
dc.date.accessioned2026-07-07T12:51:56Z
dc.date.available2026-07-07T12:51:56Z
dc.descriptionLet $R$ be a noetherian ring, $\fa$ an ideal of $R$, and $M$ an $R$--module. We prove that for a finite module $M$, if $\LC^{i}_{\fa}(M)$ is minimax for all $i\geq r\geq 1$, then $\LC^{i}_{\fa}(M)$ is artinian for $i\geq r$. A Local-global Principle for minimax local cohomology modules is shown. If $\LC^{i}_{\fa}(M)$ is coatomic for $i\leq r$ ($M$ finite) then $\LC^{i}_{\fa}(M)$ is finite for $i\leq r$. We give conditions for a module, which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing theorems are proved for local cohomology modules.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0903.2235
dc.identifierhttp://arxiv.org/abs/0903.2235
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223148
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13D45; 13D07
dc.titleOn the vanishing, artinianness and finiteness of local cohomology modules
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