On Galois cohomology of p-adic fields.

This work follows J.-M. Fontaine's paper in the Grothendieck Festschrift, where he constructs an equivalence between the category of Z(P)-adic representations of the absolute Galois group G(K), of a local field K of mixed characteristic (0, p > 0) and a category uf modules over a certain ring, endowed with two operators satisfying special properties. We give here an explicit construction of the cohomology groups of a Z(P)-adic representation of G(K) killed by a power of p, using these new objects. When K is a finite extension of Q(P), we show then how one can find again Tate's classical results about these groups : the finiteness and the calculation of the Euler-Poincare characteristic. The methods used seem to be lather simpler than the standard cohomological arguments because we dont need sophisticated theories like local class field theory and everything is essentially explicit. One gets also interesting information about the structure of the modules associated with representations and a 3-step filtration on their Galois cohomology.