  The reduction of singularities of codimension one foliations is known in the
case of ambient dimension 2 (Seidenberg, A. (1968). Reduction of singularities
of the differential equation Ady= Bdx. American Journal of Mathematics, 90(1),
248-269) and 3 (Cano, F. (2004). Reduction of the singularities of codimension
one singular foliations in dimension three. Annals of mathematics, 160(3),
907-1011). However, in greater ambient dimension it is still an open problem.
In this work we prove the existence of local uniformization for codimension one
foliations in arbitrary ambient dimension, in the case of rational archimedean
valuations.
