论文标题
在正特征中动态莫德尔·兰特猜想的稀疏性结果
A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic
论文作者
论文摘要
我们证明了一个定量的部分结果，以支持阳性特征中动态的mordell-lang猜想（也称为DML猜想）。更准确地说，我们显示以下内容：给定特征性$ p $的字段$ k $，鉴于在有限的子字段上定义了$ k $的semiabelian品种$ x $，并具有定期的自动映射$φ：x \ longrightArrow x $定义在$ k $上定义的x $，给定x（k）$ s subvariety $ v \ subsee s subsee seleteq x x $ k $ selete x $整数$ n $使得$φ^n（α）\ in V（k）$是有限的许多算术进步的结合，以及子集$ s $与该物业的属性$ a $ a $ a $ a $（仅$ n $，$ n $，$φ$，$ a $，$α$，$ v $），因为每个正面的$ m $ $ m $，我们wayd $ $ n poste $ $ n poss $ n posteger unte $ n posteger unte $ $ n west us。 s \ colon〜n \ le m \ right \} \ le a \ cdot \ left（1+ \ log m \ right）^{\ dim v}。$$
We prove a quantitative partial result in support of the Dynamical Mordell-Lang Conjecture (also known as the DML conjecture) in positive characteristic. More precisely, we show the following: given a field $K$ of characteristic $p$, given a semiabelian variety $X$ defined over a finite subfield of $K$ and endowed with a regular self-map $Φ:X \longrightarrow X$ defined over $K$, given a point $α\in X(K)$ and a subvariety $V\subseteq X$, then the set of all non-negative integers $n$ such that $Φ^n(α)\in V(K)$ is a union of finitely many arithmetic progressions along with a subset $S$ with the property that there exists a positive real number $A$ (depending only on $N$, $Φ$, $α$, $V$) such that for each positive integer $M$, we have $$\#\left\{n\in S\colon~ n\le M\right\}\le A\cdot \left(1+\log M\right)^{\dim V}.$$
