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-folds.