Overconvergent de Rham-Witt cohomology for semistable varieties

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