论文标题
沿射击轨道上的局部高度功能在投影品种上的轨道增长
Growth of local height functions along orbits of self-morphisms on projective varieties
论文作者
论文摘要
在本文中，我们考虑限制$ \ lim_ {n \至\ infty} \ sum_ {数字字段，$ s $是有限的位置集，$λ_{y，v} $是与适当的闭合子Cheme $ y \ subset x $相关的局部高度功能，而$ h_ {h_ {h_ {h} $是$ x $的高度功能。我们提供了几何条件，该条件可确保限制为零，当$ \ dim y = 0 $并假设$ \ dim y \ y \ geq1 $时，无条件地是零。特别是，我们证明（一个是无条件的，一个人都假设Vojta的猜想）动态lang-siegel类型定理，即，$ \ mathbb {p}^{n} $在$ \ mathbb {p}^{n}上的相对大小与琐事相同。这些结果是Silverman的经典结果的更高维度的概括。
In this paper, we consider the limit $ \lim_{n \to \infty} \sum_{v\in S} λ_{Y,v}(f^{n}(x))/h_{H}(f^{n}(x)) $ where $f \colon X \longrightarrow X$ is a surjective self-morphism on a smooth projective variety $X$ over a number field, $S$ is a finite set of places, $ λ_{Y,v}$ is a local height function associated with a proper closed subscheme $Y \subset X$, and $h_{H}$ is an ample height function on $X$. We give a geometric condition which ensures that the limit is zero, unconditionally when $\dim Y=0$ and assuming Vojta's conjecture when $\dim Y\geq1$. In particular, we prove (one is unconditional, one is assuming Vojta's conjecture) Dynamical Lang-Siegel type theorems, that is, the relative sizes of coordinates of orbits on $\mathbb{P}^{N}$ are asymptotically the same with trivial exceptions. These results are higher dimensional generalization of Silverman's classical result.
