On the Vanishing of Homology with Modules of Finite Length - Bergh, Petter Andreas (Mathematica Scandinavica, 2013)
We study the vanishing of homology and cohomology of a module of finite complete intersection dimension over a local ring. Given such a module of complexity $c$, we show that if $c$ (co)homology groups with a module of finite length vanish, then all higher (co)homology groups vanish.