Overconvergent de Rham-Witt cohomology for semistable varieties

2017/11/27 by Oliver Gregory, Gregory, Oliver, Andreas Langer +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1711.09943

Abstract

We define an overconvergent version of the Hyodo-Kato complex for semistable varieties Y over perfect fields of positive characteristic, and prove that its hypercohomology tensored with ℚ recovers the log-rigid cohomology when Y is quasi-projective. We then describe the monodromy operator using the overconvergent Hyodo-Kato complex. Finally, we show that overconvergent Hyodo-Kato cohomology agrees with log-crystalline cohomology in the projective semistable case.

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• On comparison between relative log de Rham-Witt cohomology and relative log crystalline cohomology

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