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4:00 pm Tuesday, November 7, 2017 AGNT: Reduction of dynatomic curves: The good, the bad, and the irreducibleby Andrew Obus (University of Virginia) in HBH 227- The dynatomic modular curves parameterize one-parameter families of dynamical systems on P^1 along with periodic points (or orbits). These are analogous to the standard modular curves parameterizing elliptic curves with torsion points (or subgroups). For the family x^2 + c of quadratic dynamical systems, the corresponding modular curves are smooth in characteristic zero. We give several results about when these curves have good/bad reduction to characteristic p, as well as when the reduction is irreducible. We will also explain some motivation from the uniform boundedness conjecture in arithmetic dynamics.
Submitted by jb93@rice.edu |