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An integral comparison of crystalline and de Rham cohomology
Let $\mathcal{O}_K$ be a mixed characteristic complete DVR with perfect residue field $k$ and fraction field $K$. It is a celebrated result of Berthelot and Ogus that for a smooth proper formal scheme $X/\mathcal{O}_K$ there exists a comparison between the de Rham cohomology groups $\mathrm{H}^i_\ma
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