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This might be a naive question. But since I haven't seen this in any reference, I'll try to ask it here. Let $T$ be a smooth scheme over the algebraically closed field $k$ of characteristic $p>0$ (...

If you want to compute crystalline cohomology of a smooth proper variety $X$ over a perfect field $k$ of characteristic $p$, the first thing you might want to try is to lift $X$ to the Witt ring $W_k$ ...

This question was inspired by and is somewhat related to this question. In his article "Crystals and the de Rham cohomology of schemes" in the collection "Dix exposes sur la cohomologie ...

The previous version of this question was rather badly broken, and I hope this version makes some sense. There have been a few questions on MathOverflow about how much representation-theoretic ...