论文标题
P-ADIC模量空间中有限的后有限地图的离散性
Discreteness of postcritically finite maps in p-adic moduli space
论文作者
论文摘要
令$ p \ geq 2 $为素数，让$ \ mathbb {c} _p $是$ p $ - ad-adic Rational Field $ \ Mathbb {q} _p $的代数关闭的完成。令$ f_c（z）$为一个合理功能的单参数$ d \ geq 2 $，其中系数是在某些开放式磁盘$ d \ subseteq \ subseteq \ mathbb {c} {c} _p $中定义在所有参数$ c $下定义的meromorthic函数。假设有适当的稳定性条件，我们证明了$ f_c $是$ f_c $的参数是有限的（PCF），除非在某些琐碎的情况下，在$ p $ -Adic disk $ d $中彼此隔离。特别是，家庭的所有PCF参数$ f_c（z）= z^d+c $ as $ p $ - aipped aipped隔离。
Let $p \geq 2$ be a prime number and let $\mathbb{C}_p$ be the completion of an algebraic closure of the $p$-adic rational field $\mathbb{Q}_p$. Let $f_c(z)$ be a one-parameter family of rational functions of degree $d\geq 2$, where the coefficients are meromorphic functions defined at all parameters $c$ in some open disk $D\subseteq\mathbb{C}_p$. Assuming an appropriate stability condition, we prove that the parameters $c$ for which $f_c$ is postcritically finite (PCF) are isolated from one another in the $p$-adic disk $D$, except in certain trivial cases. In particular, all PCF parameters of the family $f_c(z)=z^d+c$ are $p$-adically isolated.
