A dynamical lifting problem for Galois covers has a negative solution for additive separable polynomials over algebraically closed fields of positive characteristic, together with an explicit dimension formula for the space of linear conjugacy classes containing such polynomials.
Silverman.The arithmetic of dynamical systems
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A Dynamical Lifting Problem For Additive Polynomials
A dynamical lifting problem for Galois covers has a negative solution for additive separable polynomials over algebraically closed fields of positive characteristic, together with an explicit dimension formula for the space of linear conjugacy classes containing such polynomials.