# Galois representations from pre-image trees: an arboreal survey

@article{Jones2014GaloisRF, title={Galois representations from pre-image trees: an arboreal survey}, author={Rafe Jones}, journal={arXiv: Number Theory}, year={2014} }

Given a global field K and a rational function phi defined over K, one may take pre-images of 0 under successive iterates of phi, and thus obtain an infinite rooted tree T by assigning edges according to the action of phi. The absolute Galois group of K acts on T by tree automorphisms, giving a subgroup G(phi) of the group Aut(T) of all tree automorphisms. Beginning in the 1980s with work of Odoni, and developing especially over the past decade, a significant body of work has emerged on the…

## 78 Citations

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- Mathematics
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. R.W.K. Odoni showed that the Galois group of the n -th iterate of the generic monic polynomial of degree d ≥ 2 in ﬁelds of characteristic zero is the n -folded iterated wreath product of the…

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