Good and bad reduction of dynatomic modular curves
-- Andrew Obus, February 10, 2017

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The dynatomic modular curves parameterize one-parameter families of
dynamical systems on P<sup>1</sup> 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<sup>2</sup> + 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. These results are
motivated by uniform boundedness conjectures in arithmetic dynamics,
which will be explained.