under construction
Let be a morphism of locally compact topological spaces. Then there exist a unique subfunctor of the direct image functor such that for any abelian sheaf over the sections of over are those sections for which the restriction is a proper map.
This is called the direct image with compact support.
It follows that is left exact.
Let be the map into the one point space. Then for any the abelian sheaf is the abelian group consisting of sections such that is compact. One writes and calls this group a group of sections of with compact support. If , then the fiber is isomorphic to .
Last revised on May 22, 2018 at 12:00:25. See the history of this page for a list of all contributions to it.