Galois groups of iterates of some unicritical polynomials
Volume 181 / 2017
Acta Arithmetica 181 (2017), 57-73 MSC: Primary 11R32, 37P15; Secondary 14G05. DOI: 10.4064/aa8599-8-2017 Published online: 13 October 2017
We prove that the arboreal Galois representations attached to certain unicritical polynomials have finite index in an infinite wreath product of cyclic groups, and that this index is 1 in some special cases, including a new family of quadratic polynomials. To do this, we use a combination of local techniques including the Chabauty–Coleman method and the Mordell–Weil sieve.