论文标题
Néron-Ogg-Shafarevich标准的动态类似物
A Dynamical Analogue of the Criterion of Néron-Ogg-Shafarevich
论文作者
论文摘要
我们引入了Anabelian方法来研究树木瓦伊斯（Arboreal Galois）表示形式，并采用Tamagawa的Anabelian版本的Néron-Ogg-Shafarevich标准，以产生该标准的动态类似物：未经羞辱的表示对应于满足其关键位置的良好减少形式的理性图。随后，我们根据更（动态的）传统的植树表示，追求Néron-Ogg-Shafarevich标准的动态性，该标准将未经损害的栖息地表示与动力学系统的某些分离性条件有关。最后，我们将我们的标准联系起来：Anabelian标准对应于动态标准，因为一个人在临界基因座周围变化。在途中，我们制定有效的标准，以确定哪些素数在树木代表中无限地被数字字段以及该分支的渐近生长进行了。我们以示例和应用结束，尤其是针对数字字段的动态系统。
We introduce an anabelian approach to the study of arboreal Galois representations and apply Tamagawa's anabelian version of the Néron-Ogg-Shafarevich criterion to produce a dynamical analogue of this criterion: unramified representations correspond to rational maps satisfying a strong form of good reduction in terms of their critical locus. Subsequently, we pursue a dynamical anlaogue of the Néron-Ogg-Shafarevich criterion in terms of the more (dynamically) traditional arboreal representations, which relates unramified arboreal representations to a certain separability condition on the dynamical system. Finally, we relate the our criteria: the anabelian criterion corresponds to the dynamical criterion as one varies the base point around the critical locus. Along the way we develop effective criteria to determine which primes are infinitely ramified in arboreal representations over number fields, as well as the asymptotic growth of that ramification; we conclude with examples and applications, especially to dynamical systems over number fields.
