A question for iterated Galois groups in arithmetic dynamics

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...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 64; no. 2; pp. 401 - 417
Main Authors Bridy, Andrew, Doyle, John R., Ghioca, Dragos, Hsia, Liang-Chung, Tucker, Thomas J.
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.06.2021
Cambridge University Press
Subjects
Group theory
Mathematical analysis
Polynomials
Questions
37P30
Arithmetic dynamics
iterated Galois groups
37P15
37P05
11G50
11R32
14G25
arboreal Galois representations
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ISSN0008-4395
1496-4287
DOI10.4153/S0008439520000521

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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439520000521