On the dynamical Bogomolov conjecture

Abstract: Motivated by the Manin-Mumford conjecture, established by Raynaud, and following the analogy of torsion with preperiodic points, Zhang posed a dynamical Manin-Mumford conjecture. Using a canonical height introduced by Call and Silverman he further formulated a dynamical Bogomolov conjecture. A special case of these conjectures 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 relative and uniform versions of such results. This is joint work with Harry Schmidt.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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