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11. Formal period $n$

Let $K_n=K$(points of formal period n) and let $G_n=K_n/K.$ Let \[\rho_n:G_N\rightarrow \mathbb{Z}/n\mathbb{Z} \wr S_m \] (or a subgroup fixed by $\text{Aut}(f))$ where $m\approx \deg f^n/n.$


    1. Add remark

      Problem 11.1.

      [Silverman] When is the image maximal?


        • Add remark

          Problem 11.2.

          Describe $K_n\cap K_{n'}.$ Prove that this is small.

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