Graduate Number Theory Seminar
Cara Mullen
UIC
A Further Look into the Critical Orbit Structure of $f_c(z)=z^2+c$ over $\mathbf{C}_p$
Abstract: Fix a prime $p\geq2$ and consider $f_c(z)=z^2+c$ with $c\in\mathbb{C}_p$. How is the critical portrait of $f_c$ (over $\mathbb{C}_p$) related to the critical portrait of the reduced map $\bar{f_c}$ (over the residue field $k=\overline{\mathbb{F}_p})$? Last time we considered the case when 0 was strictly periodic and found that the period cannot shrink. This time we will consider maps with a strictly pre-periodic critical point, which lead to some more interesting observations and results.
Thursday March 13, 2014 at 3:00 PM in SEO 512