Hodge-Witt decomposition of relative crystalline cohomology

Oliver Gregory; Andreas Langer

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arXiv · 2006.13550

Hodge-Witt decomposition of relative crystalline cohomology

Oliver Gregory·Andreas Langer

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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, varieties of K3 type and some Calabi-Yau $n$-folds.

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Oliver Gregory, Andreas Langer. 2020-06-24. Hodge-Witt decomposition of relative crystalline cohomology. https://arxiv.org/abs/2006.13550

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