Abstract: Post-critically finite maps are described as dynamical analogs of CM Abelian Varieties. CM abelian varieties defined over the complex numbers are algebraic, and we know they have everywhere good reduction in some finite extension of their base field. This motivates us to ask the question: do PCF maps have good reduction? We will review the basics of good reduction, discuss useful properties of reduction in arithmetic dynamics, and explore the reduction of post-critically finite polynomials.
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