Analytic Galois Automorphisms

10/04/2011 - 12:15pm
10/04/2011 - 1:10pm
Ghassan Sarkis (Pomona College)

Given an arithmetic dynamical system consisting of a commuting pair of power series over the $p$-adic integers, we consider the tower of field extensions generated by the points of this dynamical system.  In a sense, the power series correspond to "globally analytic" Galois automorphisms, and we ask: when is the Galois group of the tower "global?"  In exploring the answer, we survey tools from the theory of the fields of norms, constructions from standard local class field theory using Lubin-Tate groups, and a conjecture of Lubin's that motivates the question.  This is joint work with Joel Specter arising from the Claremont Colleges Math REU. 

ML 134