  Given a polynomial f of degree d defined over a complete local field, we
construct a biholomorphic change of variables defined in a neighbourhood of
infinity which transforms the action z->f(z) to the multiplicative action
z->z^d. The relation between this construction and the Bottcher coordinate in
complex polynomial dynamics is similar to the relation between the complex
uniformization of elliptic curves, and Tate's p-adic uniformization.
Specifically, this biholomorphism is Galois equivariant, reducing certain
questions about the Galois theory of preimages by f to questions about
multiplicative Kummer theory.
