Reduction of dynatomic curves

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• Holly Krieger (University of Cambridge)
• Tuesday 06 June 2017, 14:30-15:30
• MR13.

If you have a question about this talk, please contact G. Rosso.

Dynatomic curves parametrize n-periodic orbits of a one-parameter family of polynomial dynamical systems. These curves lack the structure of their arithmetic-geometric analogues (modular curves of level n) but can be studied dynamically. Morton and Silverman conjectured a dynamical analogue of the uniform boundedness conjecture (theorems of Mazur, Merel), asserting uniform bounds for the number of rational periodic points for such a family. I will discuss recent work towards the function field version of their conjecture, including results on the reduction mod p of dynatomic curves for the quadratic polynomial family z^2+c.

This talk is part of the Number Theory Seminar series.

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