Rendiconti del Seminario Matematico della Università di Padova


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Volume 137, 2017, pp. 229–235
DOI: 10.4171/RSMUP/137-13

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

Andreas Langer[1] and Thomas Zink[2]

(1) University of Exeter, UK
(2) Universität Bielefeld, Germany

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.

Keywords: Log-crystalline cohomology, de Rham–Witt complex

Langer Andreas, Zink Thomas: 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), 229-235. doi: 10.4171/RSMUP/137-13