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14. Inverse Arboreal Galois Problem (IAGP)


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      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.


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          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.