On the vanishing of homology for modules of finite complete intersection dimension

Abstract

We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which generalizes phenomena for modules of finite complete intersection dimension and complexity one. Using this concept, we prove results on length and vanishing of homology modules.

12 pages