Geodesic
Galois groups of iterates of some unicritical polynomials
Michael R. Bush 1   ; Wade Hindes 2   ; Nicole R. Looper 3
1 Department of Mathematics Washington & Lee University 204 W. Washington Street Lexington, VA 24450, U.S.A.
2 Department of Mathematics The Graduate Center City University of New York (CUNY) 365 Fifth Avenue New York, NY 10016, U.S.A.
3 Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208, U.S.A.
Acta Arithmetica, Tome 181 (2017) no. 1, pp. 57-73 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa8599-8-2017
Keywords: prove arboreal galois representations attached certain unicritical polynomials have finite index infinite wreath product cyclic groups index special cases including family quadratic polynomials combination local techniques including chabauty coleman method mordell weil sieve

Michael R. Bush  1   ; Wade Hindes  2   ; Nicole R. Looper  3

1 Department of Mathematics Washington & Lee University 204 W. Washington Street Lexington, VA 24450, U.S.A.
2 Department of Mathematics The Graduate Center City University of New York (CUNY) 365 Fifth Avenue New York, NY 10016, U.S.A.
3 Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208, U.S.A. 
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     author = {Michael R. Bush and Wade Hindes and Nicole R. Looper},
     title = {Galois groups of iterates of some unicritical polynomials},
     journal = {Acta Arithmetica},
     pages = {57--73},
     year = {2017},
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Michael R. Bush; Wade Hindes; Nicole R. Looper. Galois groups of iterates of some unicritical polynomials. Acta Arithmetica, Tome 181 (2017) no. 1, pp. 57-73. doi: 10.4064/aa8599-8-2017

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