Local Arboreal Representations
Local Arboreal Representations
Let |$K$| be a field complete with respect to a discrete valuation |$v$| of residue characteristic |$p$|. Let |$f(z) \in K[z]$| be a separable polynomial of the form |$z^\ell-c$|. Given |$a \in K$|, we examine the Galois groups and ramification groups of the extensions of |$K$| generated by the solutions …