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Quote from Kim and Hain I think: The Hyodo-Kato thm relates de Rham coh of a variety over a local field (with semistable red) to the log crystalline cohomology of the special fiber: H dR i(X F)≅H cr i(Y/W)⊗ WFH^i_{dR}(X_F) \cong H^i_{cr}(Y/W) \otimes_W F
nLab page on Log crystalline cohomology