论文标题
最小模型程序在算术动力学中的某些应用
Some applications of the minimal model program in arithmetic dynamics
论文作者
论文摘要
我们描述了一项通用计划，用于研究代数品种的溢流性内态性动力学，这些动态与最小模型程序的技术相适应。我们获得了承认内态性内态性质的圆周内形态性的周期前点的密度结果，并使用我们的方法将Medvedev-Scanlon猜想的某些情况降低为所谓的Q-Abelian品种。我们还提供了具有积极熵的自动形态的存在与多样性的连接组件之间的联系。特别是，我们表明，如果$ x $是正常的，并且具有有限生成的nef锥的投射，则$ x $具有正熵的自动形态，并且仅当且仅当连接组件的组$π_0\ aut（x）$具有无限顺序的要素。
We describe a general program for studying the dynamics of surjective endomorphisms of algebraic varieties that are amenable to techniques from the minimal model program. We obtain density results on the pre-periodic points of surjective endomorphisms of varieties admitting an int-amplified endomorphism, and reduce certain cases of the Medvedev-Scanlon conjecture to so called Q-abelian varieties using our approach. We also provide a connection between the existence of an automorphism with positive entropy and group of connected components of a variety. In particular, we show that if $X$ is normal and projective with finitely generated nef cone then $X$ has an automorphism of positive entropy if and only if the group of connected components $π_0\Aut(X)$ has an element of infinite order.
