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math.NT2021
Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity
Philipp Habegger, Harry Schmidt
In a recent breakthrough, Dimitrov solved the Schinzel-Zassenhaus Conjecture. We follow his approach and adapt it to certain dynamical systems arising from polynomials of the form…
math.NT2021
Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties
Fabrizio Barroero, Lars Kühne, Harry Schmidt
Let be a semiabelian variety and a curve in that is not contained in a proper algebraic subgroup of . In this situation, conjectures of Pink and Zilber imply that th…
math.NT2021
Lower bounds for Galois orbits of special points on Shimura varieties: a point-counting approach
Gal Binyamini, Harry Schmidt, Andrei Yafaev
Let be a Shimura variety and let be a Weil height function on . We conjecture that the heights of special points in are discriminant negligible. Assuming this conjec…