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The Vojta conjecture implies Galois rigidity in dynamical families

Author: Wade Hindes
Journal: Proc. Amer. Math. Soc. 144 (2016), 1931-1938
MSC (2010): Primary 14G05, 37P55; Secondary 11R32
Published electronically: December 15, 2015
MathSciNet review: 3460156
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Abstract: We show that the Vojta (or Hall-Lang) conjecture implies that the arboreal Galois representations in a 1-parameter family of quadratic polynomials are surjective if and only if they surject onto some finite and uniform quotient. As an application, we use the Vojta conjecture, our uniformity theorem over $ \mathbb{Q}(t)$, and Hilbert's irreducibility theorem to prove that the prime divisors of many quadratic orbits have density zero.

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Additional Information

Wade Hindes
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912

Keywords: Rational points on curves, arithmetic dynamics, Galois theory
Received by editor(s): January 7, 2015
Received by editor(s) in revised form: June 16, 2015
Published electronically: December 15, 2015
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2015 American Mathematical Society

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