Extensions of local fields and truncated power series

الأصل · EN

Let K be a finite tamely ramified extension of ₚ and let L/K be a totally ramified (/pⁿ)-extension. Let πₗ be a uniformizer for L, let σ be a generator for (L/K), and let f(X) be an element of Øₖ[X] such that σ(πₗ)=f(πₗ). We show that the reduction of f(X) modulo the maximal ideal of Øₖ determines a certain subextension of L/K up to isomorphism. We use this result to study the field extensions generated by periodic points of a p-adic dynamical system.