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

TL;DR

This paper establishes new rigidity results for the vanishing of stable (co)homology in modules with finite complete intersection dimension, introducing pre-rigidity to generalize existing phenomena and derive new vanishing criteria.

Contribution

It generalizes known vanishing results by introducing the concept of pre-rigidity for modules of finite complete intersection dimension and complexity one.

Findings

Proves rigidity results for stable (co)homology vanishing

Introduces the notion of pre-rigidity for modules

Derives new results on length and vanishing of homology modules

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.