A neighborhood of the zero section of the normal bundle of an embedded complex manifold can be seen as a first-order approximation of a neighborhood of the embedded manifold. One would like to know if these two neighborhoods are biholomorphically equivalent. This can be realized as a linearization problem. There are formal obstructions
to the linearization. The Grauert's formal principle is to determine whether the two neighborhoods are holomorphically equivalent when formal obstructions vanish. We will present convergence results under small divisors conditions similar to those in local complex dynamical systems, but in the form represented via cohomology groups in connection with tangent and normal bundles of the embedded manifold. This is joint work with Laurent Stolovich.