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A question for iterated Galois groups in arithmetic dynamics

Part of: Algebraic number theory: global fields Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry Arithmetic and non-Archimedean dynamical systems

Published online by Cambridge University Press:  10 July 2020

Andrew Bridy ,
John R. Doyle ,
Dragos Ghioca ,
Liang-Chung Hsia  and
Thomas J. Tucker
Andrew Bridy
Affiliation:
Departments of Political Science and Computer Science, Yale University, New Haven, CT06511, USA e-mail: [email protected]
John R. Doyle
Affiliation:
Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA71272, USA e-mail: [email protected]
Dragos Ghioca*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BCV6T 1Z2, Canada
Liang-Chung Hsia
Affiliation:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, ROC e-mail: [email protected]
Thomas J. Tucker
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY14620, USA e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

We formulate a general question regarding the size of the iterated Galois groups associated with an algebraic dynamical system and then we discuss some special cases of our question. Our main result answers this question for certain split polynomial maps whose coordinates are unicritical polynomials.

Keywords

Arithmetic dynamicsarboreal Galois representationsiterated Galois groups

MSC classification

Primary: 37P15: Global ground fields
Secondary: 11G50: Heights 11R32: Galois theory 14G25: Global ground fields 37P05: Polynomial and rational maps 37P30: Height functions; Green functions; invariant measures
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 401 - 417
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

D.G. was partially supported by an NSERC Discovery grant. L.-C. H. was partially supported by MOST Grant 108-2115-M-003-005-MY2.

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