On cohomologically complete intersections

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dc.creatorHellus, Michael
dc.creatorSchenzel, Peter
dc.date2008-04-16
dc.date.accessioned2026-07-07T09:32:56Z
dc.date.available2026-07-07T09:32:56Z
dc.descriptionAn ideal $I$ of a local Gorenstein ring $(R, \mathfrak m)$ is called cohomologically complete intersection whenever $H^i_I(R) = 0$ for all $i \not= \height I.$ Here $H^i_I(R), i \in \mathbb Z,$ denotes the local cohomology of $R$ with respect to $I.$ For instance, a set-theoretic complete intersection is a cohomologically complete intersection. Here we study cohomologically complete intersections from various homological points of view, in particular in terms of their Bass numbers of $H^c_I(R), c = \height I.$ As a main result it is shown that the vanishing $H^i_I(R) = 0$ for all $i \not= c$ is completely encoded in homological properties of $H^c_I(R),$ in particular in its Bass numbers.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/0804.2558
dc.identifierhttp://arxiv.org/abs/0804.2558
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158959
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13D45; 14M10; 13C40
dc.titleOn cohomologically complete intersections
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