$\mathbb{P}^{1}$上动力系统的定义域：Silverman结果的改进

Giulio Bresciani

$\mathbb{P}^{1}$上动力系统的定义域：Silverman结果的改进

数论 2024-05-13 v2 代数几何动力系统

作者: Giulio Bresciani

摘要

J. Silverman证明了 $\mathbb{P}^{1}$ 上的动力系统如果是多项式或具有偶数次数，则下降到模域，但对于奇数次的非多项式系统，情况尚不明确。我们给出了 $\mathbb{P}^{1}$ 上哪些动力系统下降到模域的完整刻画。

关键词

射影直线上的动力系统模域定义域 Silverman定理多项式次数偶数次数

引用

@article{arxiv.2405.03612,
  title  = {Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman},
  author = {Giulio Bresciani},
  journal= {arXiv preprint arXiv:2405.03612},
  year   = {2024}
}

备注

There is a mistake in the proof of the main theorem. In the middle of page 5, we state that \phi has equal orders of vanishing in 0 and \infty. However, the argument only proves the weaker statement that the ramification degrees are equal. This is not sufficient to conclude

$\mathbb{P}^{1}$上动力系统的定义域：Silverman结果的改进

摘要

关键词

引用

备注

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