Uniformity in the dynamical Bogomolov conjecture

Abstract: Zhang has proposed dynamical versions of the classical Manin- Mumford and Bogomolov conjectures. A special case of these conjectures, for ‘split’ maps, has recently been established by Nguyen, Ghioca and Ye. In particular, they show that two rational maps have at most finitely many common preperiodic points, unless they are ‘related’. In this talk we discuss uniform versions of their results across 1-parameter families of certain split maps and curves. This is joint work with Harry Schmidt.

number theory

Audience: researchers in the topic

Columbia CUNY NYU number theory seminar