  The purpose of this article is to give formulas for Bloch-Kato's exponential
map and its dual for an absolutely crystalline p-adic representation V, in
terms of the (phi,Gamma)-module associated to that representation. As a
corollary of these computations, we can give a very simple (and slightly
improved) description of Perrin-Riou's exponential map (which interpolates
Bloch-Kato's exponentials for V(k)). This new description directly implies
Perrin-Riou's reciprocity formula.
