Galois representations from pre-image trees: an arboreal survey

  title={Galois representations from pre-image trees: an arboreal survey},
  author={Rafe Jones},
  journal={arXiv: Number Theory},
  • Rafe Jones
  • Published 2014
  • Mathematics
  • arXiv: Number Theory
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… Expand
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