On cohomologically complete intersections

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• 作者：Michael Hellus ; Peter Schenzel
• 关键词：Local cohomology ; Complete intersections ; Cohomological dimension
• 刊名：Journal of Algebra
• 出版年：2008
• 出版时间：15 November 2008
• 年：2008
• 卷：320
• 期：10
• 页码：3733-3748
• 全文大小：233 K

文摘

An ideal I of a local Gorenstein ring () is called cohomologically complete intersection whenever for all i≠heightI. Here , , 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 , c=heightI. As a main result it is shown that the vanishing for all i≠c is completely encoded in homological properties of , in particular in its Bass numbers.