Fabrizzio Andreatta (Milano)
TITLE: Fontaine's crystalline conjecture revisited.
ABSTRACT (joint work with O. Brinon and A. Iovita):
Let $K$ be a local field with ring of integers $O_K$ such that $p$
generates the maximal ideal of $O_K$.
Given a proper and smooth scheme $X$ over $O_K$, I will prove a
comparison isomorphism between the \'etale cohomology of $X_\Kbar$
and the de Rham cohomology of $X_K$.
Our approach is based both on Faltings' approach and on Fontaine's
theory in the relative setting as developed by O. Brinon.