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In this note we derive for a smooth projective variety with normal crossing divisor 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 the crystalline cohomology and overconvergent de Rham–Witt cohomology are canonically isomorphic.
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Andreas Langer, Thomas Zink, A comparison of logarithmic overconvergent de Rham–Witt and log-crystalline cohomology for projective smooth varieties with normal crossing divisor. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 229–235