On the vanishing of (co)homology for modules admitting certain filtrations

Abstract

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations and generalize a theorem of Celikbas-Takahashi. Our work produces new classes of rigid and test modules, particularly over local rings of prime characteristic. Additionally, it provides applications in the study of torsion in tensor products of modules, including a conjecture of Huneke-Wiegand.