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4. Dynatomic Modular Curves


    1. Add remark

      Problem 4.1.

      [Andrew Obus]
      1. Analogy between dynatomic and modular curves (See Silverman, ADS Section 4.1 and 4.2 for dynatomic polynomials).
      2. What are other proxies for level structure, e.g. marked critical points, for which bad primes are more natural?


        • Add remark

          Problem 4.2.

          1. For $p|N,$ $X^{\text{dyn}}(N)$ has bad reduction at $p$ for the standard model, but evidence suggests there exists a different model with good reduction. Is this true? If not, why not? Is there a “reason" for this to be true?
          2. (Silverman) In general, what are the primes of bad reduction and why?

              Cite this as: AimPL: The Galois theory of orbits in arithmetic dynamics, available at http://aimpl.org/galarithdyn.