论文标题
VOJTA的猜想，与亚物体相关的高度以及算术动力学中的原始质量除数
Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics
论文作者
论文摘要
假设VOJTA的猜想，我们为极限\ [\ lim_ {n \ to \ infty} \ frac {光滑的投射品种$ x $，$ h_ {h} $上的透明自我塑态是$ x $上的充分高度功能，而$ h_ {y} $是与封闭的codimension of Codimension x $相关的全局高度函数。基于此，我们提出了一个猜想，使限制为零。我们指出，我们的猜想意味着在$ \ mathbb {p}^{2} _ {\ overline {\ mathbb {q}}} $上的内态构态性的动态mordell-lang猜想。我们还讨论了VOJTA的猜想的应用，并在截短的计数函数上讨论了存在$ f $轨道坐标的原始素数分隔的问题
Assuming Vojta's conjecture, we give a sufficient condition for the limit \[ \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x))} \] is equal to zero, where $f \colon X \longrightarrow X$ is a surjective self-morphism on a smooth projective variety $X$, $h_{H}$ is an ample height function on $X$, and $h_{Y}$ is a global height function associated with a closed subscheme $Y \subset X$ of codimension at least two. Based on this, we propose a conjecture on a sufficient condition for the limit to be zero. We point out that our conjecture implies Dynamical Mordell-Lang conjecture for endomorphisms on $\mathbb{P}^{2}_{\overline{\mathbb{Q}}}$. We also discuss applications of Vojta's conjecture with truncated counting function to the problem of the existence of primitive prime divisors of coordinates of orbits of $f$
