English

Galois groups of iterates of some unicritical polynomials

Number Theory 2016-08-12 v1

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 we prove surjectivity for some small degree examples, 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.

Keywords

Cite

@article{arxiv.1608.03328,
  title  = {Galois groups of iterates of some unicritical polynomials},
  author = {Michael R. Bush and Wade Hindes and Nicole R. Looper},
  journal= {arXiv preprint arXiv:1608.03328},
  year   = {2016}
}