Arboreal Galois representations
Arboreal Galois representations
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DOI：
10.1007/s10711-006-9113-9
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发表时间：
2007
影响因子：
0.5
通讯作者：
Rafe Jones
中科院分区：
文献类型：
--
作者：
N. Boston;Rafe Jones
Let $$G_{\mathbb{Q}}$$ be the absolute Galois group of $$\mathbb{Q}$$, and let T be the complete rooted d-ary tree, where d ≥ 2. In this article, we study “arboreal” representations of $$G_{\mathbb{Q}}$$ 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 $$G_\mathbb{Q}$$. 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 $$G_{\mathbb{Q}}$$. 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 $$G_{\mathbb{Q}}$$.
