On cohomologically complete intersections

Details On cohomologically complete intersections On cohomologically complete intersections

2008-04-16

arxiv.org/abs/0804.2558v1

Mathematics

Commutative Algebra

16 pages

Scientific paper

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 $i \not= c$ is completely encoded in homological properties of $H^c_I(R),$ in particular in its Bass numbers.

Affiliated with

Also associated with

No associations

Rating

On cohomologically complete intersections does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On cohomologically complete intersections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On cohomologically complete intersections will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-607140