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Degree gaps for multipliers and the dynamical André–Oort conjecture

Part of: Arithmetic and non-Archimedean dynamical systems

Published online by Cambridge University Press:  13 November 2020

Patrick Ingram
Patrick Ingram*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ONM3J 1P3, Canada
*
e-mail:[email protected]
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Abstract

We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multiplier of very low degree, except those that vanish, generalizing results of Baker and DeMarco, and Favre and Gauthier.

Keywords

Arithmetic dynamicscritical heightunlikely intersections

MSC classification

Primary: 37P45: Families and moduli spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 867 - 876
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Copyright
© Canadian Mathematical Society 2020

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References

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