11 citations · 18 across the 13 of their papers we have counts for
18 papers
Dynamical Canonical Heights and Finite Trees
Philipp Habegger, Harry Schmidt
We establish lower bounds for the canonical height of a wandering point that decays like the square of the field degree. Our methods and results apply to centered, postcritically f…
Uniform sum-product phenomenon for algebraic groups and Bremner's conjecture
Joseph Harrison, Akshat Mudgal, Harry Schmidt
In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this…
On the Manin-Mumford Theorem for Algebraic Groups
Harry Schmidt, Immanuel van Santen
We describe the Zariski-closure of sets of torsion points in connected algebraic groups. This is a generalization of the Manin-Mumford conjecture for commutative algebraic groups p…
An effective Pila-Wilkie theorem for sets definable using Pfaffian functions, with some diophantine applications
Gal Binyamini, Gareth O. Jones, Harry Schmidt +1
We prove an effective version of the Pila-Wilkie Theorem for sets definable using Pfaffian functions, providing effective estimates for the number of algebraic points of bounded he…
Height coincidences in products of the projective line
Niki Myrto Mavraki, Harry Schmidt, Robert Wilms
We consider hypersurfaces in that contain a generic sequence of small dynamical height with respect to a split map and project onto coordinates. We show th…
On the dynamical Bogomolov conjecture for families of split rational maps
Niki Myrto Mavraki, Harry Schmidt
We prove that Zhang's dynamical Bogomolov conjecture holds uniformly along -parameter families of rational split maps and curves. This provides dynamical analogues of recent res…