Extensions de valuation et polygone de Newton

— Let (K, ν) be a valued field and L a finite cyclic extension of K defined by L = K[x]/(P ), then any valuation of L which extends ν defines a pseudo-valuation ζ onK[x] whose kernel is the principal ideal (P ). We know how to associate to ζ a family of valuations on K[x], called an admissible family, which is explicitely constructed by augmented valuations and limit augmented valuations. We give a necessary and sufficient condition for a valuation of K[x] to belong to an admissible family associated to a pseudo-valuation ζ which corresponds to a valuation of L, this condition depends only on the polynomial P . On the way we can determine all the valuations of L which extend the valuation ν of K. To give this condition we define the Newton polygon associated to P , to a polynomial φ and to a valuation μ of K[x].