Fabrizzio Andreatta (Milano) <BR><BR>


TITLE: Fontaine's crystalline conjecture revisited.<BR><BR>


ABSTRACT (joint work with O. Brinon and A. Iovita):<BR>

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.