
## 12. Study wild ramification in arboreal Galois representations

1. #### Problem 12.1.

[Jones] Say something interesting about wild ramification for arboreal representations. e.g. study Galois representations over local fields of residue characteristic dividing degree of $f$ (or even less than or equal to the degree). e.g. An arboreal version of Sen’s theorem.
• #### Problem 12.2.

Let $f(z)=z^2+1$ over $\mathbb{Q}_2.$ What is the size, etc, of the arboreal representation?

Cite this as: AimPL: The Galois theory of orbits in arithmetic dynamics, available at http://aimpl.org/galarithdyn.