论文标题
完整的Metrized场上有理图的拓扑熵
Topological entropy of a rational map over a complete metrized field
论文作者
论文摘要
我们证明，在完整的非Archimedean领域定义的投射品种的任何主要理性自图的拓扑熵与最大动力学学位的最大限制，从而扩展了Gromov和Dinh-Sbibony的定理，并从复合体到非Archimedean设置。我们通过证明任何常规的自图承认在估值环上定义的投影模型的任何常规自图都必须为零熵。为此，我们介绍了伯科维奇分析空间的电子还原，这是一个独立利益的概念。
We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum of its dynamical degrees, thereby extending a theorem of Gromov and Dinh-Sibony from the complex to the non-Archimedean setting. We proceed by proving that any regular self-map which admits a regular extension to a projective model defined over the valuation ring has necessarily zero entropy. To this end we introduce the e-reduction of a Berkovich analytic space, a notion of independent interest.
