
## 14. Inverse Arboreal Galois Problem (IAGP)

1. #### Problem 14.1.

[Faber] Work over $\mathbb{C}(x)$ for a start. Given a subgroup $G\subseteq \text{Aut}$(regularly rooted $d$-ary tree). Does there exist a polynomial $f(z)\in K[z]$ with $G$ as its image of Galois representation? Interpret and solve.
• #### Problem 14.2.

Variation of problem 14.1: ask again only in a dynatomic setting. Formulate and solve.

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