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math.NT2019
Uniform Manin-Mumford for a family of genus 2 curves
Laura DeMarco, Holly Krieger, Hexi Ye
We introduce a general strategy for proving quantitative and uniform bounds on the number of common points of height zero for a pair of inequivalent height functions on $\mathbb{P}…
math.NT2017★ 1 cited
Bounded height in families of dynamical systems
Laura DeMarco, Dragos Ghioca, Holly Krieger +3
Let a and b be algebraic numbers such that exactly one of a and b is an algebraic integer, and let f_t(z):=z^2+t be a family of polynomials parametrized by t. We prove that the set…
math.NT2016
The Dynamical Andre-Oort Conjecture for cubic polynomials
Dragos Ghioca, Hexi Ye
In the moduli space of degree d polynomials, the special subvarieties are those cut out by critical orbit relations, and then the special points are the post-critically finite poly…