Reduction of post-critically finite polynomials

Abstract: Post-critically finite maps are described as dynamical analogs of CM Abelian Varieties. A CM abelian varieties over a number field $K$ has everywhere good reduction in some finite extension $L/K$. This motivates us to ask the question: do PCF maps have good reduction? We can use a particular family of maps, dynamical Belyi polynomials, to provide necessary and sufficient conditions for a PCF polynomial of degree $d$ to have potential good reduction at a prime $p$. This is joint work with Jacqueline Anderson and Michelle Manes.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

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