Periodic points in towers of finite fields for rational maps associated to supersingular elliptic curves

04/24/2018 - 12:15pm
04/24/2018 - 1:10pm
Bianca Thompson (HMC)

In arithmetic dynamics we are interested in classifying and counting points that live in cycles or eventually live in cycles for a family of maps over a given field. We refer to each of these types of points as periodic or preperiodic, respectively. Over a finite field, everything is preperiodic, so the questions becomes what can we say about the number points that are periodic. We'll talk about a family of rational maps associated to supersingular elliptic curves and give preliminary results on what we can say about the number of periodic points over \FF_{p^n}, for some prime p.

Millikan 2099, Pomona College

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