Hodge–Witt decomposition of relative crystalline cohomology

Abstract

For a smooth and proper scheme over an Artinian local ring with ordinary reduction over the perfect residue field, we prove — under some general assumptions — that the relative de Rham–Witt spectral sequence degenerates and the relative crystalline cohomology, equipped with its display structure arising from the Nygaard complexes, has a Hodge–Witt decomposition into a direct sum of (suitably Tate-Twisted) multiplicative displays. As examples, our main results include the cases of abelian schemes, complete intersections, surfaces, varieties of K3 type and some Calabi–Yau n $n$ -folds.