On cohomologically complete intersections

Abstract

An 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 $i\ne c$ is completely encoded in homological properties of $H_I^c(R),$ in particular in its Bass numbers.

16 pages

References in corpus (1)

• Local Cohomology and Matlis duality

Cited by in corpus (1)

• On endomorphism rings and dimensions of local cohomology modules