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16 votes
1 answer
984 views

Reconstruct a variety from its crystalline topos

Let $k$ be a perfect field of positive characteristic. Let $X$ be a smooth projective geometrically connected $k$-scheme with a $k$-point. Can we reconstruct $X$ from its small crystalline topos $((X/...
6 votes
0 answers
467 views

Torsionfree crystalline cohomology implies torsionfree etale cohomology?

Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$. Let $W=W(k)$ be the ring of Witt vectors of $k$. Assume that the crystalline cohomology $H^2_{...