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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

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.

Authors

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

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