A note on ρ-adic etale cohomology

1o Let X be a projective smooth scheme over a complete discrete valuation ring A o2 mixed characteristics (0, p).In [2], Fontaine and Messing studied the relation between the p-adic etale cohomology o the generic fiber H(X)-H(X(R), Z) ( is an algebraic closure o2 ]) and the crystalline cohomology of the special fiber H(X).In this article, we consider not Gal(/v)-representation H(X), but H(X) itsel and study this cohomology group by using the syntomic cohomology introduced in [2].Detailed studies containing the complete proof will appear elsewhere.We will use the 2ollowing notation" X is a projective, smooth and geo- metrically connected scheme over A of dimension d as above, and Y-X