Questions tagged [crystalline-cohomology]

I'm reading Illusie's survey on Crystalline cohomology, and I found him talking about those $p$-adic period rings like $B_{\text{dR}}, B_{\text{cris}}$. Can anybody explain what they are and give some ...

I have been looking for several weeks for the exact and the precise statement of Ogus conjecture, but, I cannot find it. The only book which made me discover the statement of this conjecture is that ...

Hello, Let $k$ be a field of characteristic $p > 0$, and let $Y$ be a $k$-scheme. Consider the sites $Y_{syn}$ and $(Y/W_n)_{cris}$ (where $W_n$ are the Witt vectors of $k$ of length $n$), of $Y$ ...

The following may be well-known (or obviously false), but I can't find a counterexample or a reference. Suppose that $k$ is some perfect field (one can assume algebraically closed, if that makes you ...

Excuse me if this question is trivial or trivially false, or not at this sites level. Lets work over an algebraically closed field of characteristic $p>0$, say $k$. The action of the Frobenius on $...

On the link, page, $ 2 $, the Berthlot-Ogus isomorphism theorem is stated as follows, We have a canonical isomorphism, $$ \rho_{\mathrm{cris}} \ : \ H_{\mathrm{cris}}^{i} (X) \otimes_{K_ {0}} K \to H_{...