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Galois groups of iterates of some unicritical polynomials

Volume 181 / 2017

Michael R. Bush, Wade Hindes, Nicole R. Looper 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.


  • Michael R. BushDepartment of Mathematics
    Washington & Lee University
    204 W. Washington Street
    Lexington, VA 24450, U.S.A.
  • Wade HindesDepartment of Mathematics
    The Graduate Center
    City University of New York (CUNY)
    365 Fifth Avenue
    New York, NY 10016, U.S.A.
  • Nicole R. LooperDepartment of Mathematics
    Northwestern University
    2033 Sheridan Road
    Evanston, IL 60208, U.S.A.

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