论文标题
$ p $ - 在理性地图下的轨道插值
$p$-Adic interpolation of orbits under rational maps
论文作者
论文摘要
令$ l $为特征零的字段，令$ h：\ mathbb {p}^1 \ to \ mathbb {p}^1 $是定义在$ l $上的有理图，然后让$ c \ in \ mathbb {p}^1（l）$。我们表明，存在有限生成的子字段$ k $ $ l $，$ c $和$ h $都被定义了一套无限的非等价非架构的非架构的$ k _ {\ mathfrak {p Mathfrak {p}} $，其中有一个正integer $ a = a = a = a = a = a = a = a = a = p} \ {0，\ ldots，a-1 \} $存在power系列$ g_i（t）\ in k _ {\ mathfrak {\ mathfrak {p}} [[t]] $在$ k _ {\ mathfrak {p}} $ y y $ k _ {\ mathfrak {p}}的封闭式单位光盘上收敛于$ k _ { $ n $。结果，我们表明，动态的mordell-lang猜想适用于$ \ mathbb {p}^1 \ times x $的拆分自动地图$（h，g）$，带有$ g $étale。
Let $L$ be a field of characteristic zero, let $h:\mathbb{P}^1\to \mathbb{P}^1$ be a rational map defined over $L$, and let $c\in \mathbb{P}^1(L)$. We show that there exists a finitely generated subfield $K$ of $L$ over which both $c$ and $h$ are defined along with an infinite set of inequivalent non-archimedean completions $K_{\mathfrak{p}}$ for which there exists a positive integer $a=a(\mathfrak{p})$ with the property that for $i\in \{0,\ldots ,a-1\}$ there exists a power series $g_i(t)\in K_{\mathfrak{p}}[[t]]$ that converges on the closed unit disc of $K_{\mathfrak{p}}$ such that $h^{an+i}(c)=g_i(n)$ for all sufficiently large $n$. As a consequence we show that the dynamical Mordell-Lang conjecture holds for split self-maps $(h,g)$ of $\mathbb{P}^1 \times X$ with $g$ étale.
