A comparison of logarithmic overconvergent de Rham–Witt and log-crystalline cohomology for projective smooth varieties with normal crossing divisor

Abstract

In this note we derive for a smooth projective variety $X$ with normal crossing divisor $Z$ an integral comparison between the log-crystalline cohomology of the associated log-scheme and the logarithmic overconvergent de Rham–Witt cohomology defined by Matsuue. This extends our previous result that in the absence of a divisor $Z$ the crystalline cohomology and overconvergent de Rham–Witt cohomology are canonically isomorphic.