From Manin–Mumford to dynamical rigidity

Abstract: In the early 1980s, Raynaud proved a theorem (the Manin–Mumford Conjecture) about the geometry of torsion points in abelian varieties, using number-theoretic methods. Around the same time, and with completely different methods, McMullen proved a theorem about dynamical stability for maps on $\mathbb{P}^1$. In new work, joint with Myrto Mavraki, we view these results as special cases of a unifying conjecture. The conjectural statement is directly inspired by a recent theorem of Gao and Habegger (called Relative Manin–Mumford) and results in complex dynamics of Dujardin, Gauthier, Vigny, and others.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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