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
Abstract
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.
