Higher displays arising from filtered de Rham-Witt complexes

Abstract

For a smooth projective scheme X over a ring R where p is nilpotent that meets some general assumptions we prove that the crystalline cohomology is equipped with the structure of a higher display, Frobenius-divisibility is induced by the Nygaard filtration on the relative de Rham-Witt complex. We also prove that under more restrictive assumptions there is a crystal of relative displays associated to PD-tickenings.