The embedding conjecture for quasi-ordinary hypersurfaces

This paper has two objectives: we first generalize the theory of Abhyankar–Moh to quasi-ordinary polynomials, then we use the notion of approximate roots and that of generalized Newton polygons in order to prove the embedding conjecture for this class of polynomials. This conjecture–made by S.S. Abhyankar and A. Sathaye–says that if a hypersurface of the affine space is isomorphic to a coordinate, then it is equivalent to it.