Co-Localization, Co-Support and Local Homology
A. S. Richardson · Rocky Mountain Journal of Mathematics · 2006
We propose a definition of co-support for modules over commutative, Noetherian rings that we hope will relate to the local homology functors of Greenlees and May in the same way ordinary support relates to local cohomology.By expressing local homology in terms of the Koszul complex, we prove some vanishing theorems involving this co-support.We also investigate the co-localization functor which gives rise to our definition of co-support.This functor treats Artiniantype constructions the same way the ordinary localization functor treats Noetherian-type constructions, and this duality extends to one between co-support and ordinary support.