Arboreal Galois representations |
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Authors: | Nigel Boston Rafe Jones |
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Affiliation: | (1) University of Wisconsin, Madison, WI, USA |
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Abstract: | Let be the absolute Galois group of , and let T be the complete rooted d-ary tree, where d ≥ 2. In this article, we study “arboreal” representations of into the automorphism group of T, particularly in the case d = 2. In doing so, we propose a parallel to the well-developed and powerful theory of linear p-adic representations of . We first give some methods of constructing arboreal representations and discuss a few results of other authors concerning their size in certain special cases. We then discuss the analogy between arboreal and linear representations of . Finally, we present some new examples and conjectures, particularly relating to the question of which subgroups of Aut(T) can occur as the image of an arboreal representation of . |
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Keywords: | Galois representation Rooted tree Tree automorphisms Pro-p group Iterates Monodromy groups |
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