  In this paper, we generalise the construction of the Bloch-Kato exponential
map to complete discrete valuation fields of mixed characteristic (0,p) whose
residue fields have a finite p-basis. As an application we prove an explicit
reciprocity law, extending a result of Cherbonnier and Colmez in the classical
case. This result relies on the calculation of the Galois cohomology of a
p-adic representation V in terms of its (phi,G)-module.
