论文标题
关于曲线的自我对应
On self-correspondences on curves
论文作者
论文摘要
我们研究曲线上自动对应的代数动力学。在代数封闭的字段上对（合适而平滑的）曲线$ c $的自我对应是另一个曲线$ d $的数据，两个非稳定的可分离型态度$π_1$和$π_2$从$ d $到$ c $。如果$π_1^{ - 1}（s）=π_2^{ - 1}（s）$，则$ c $的子集$ s $是完整的。我们表明，自我对应分为两个类：那些只有有限的完整集有限的类别，而$ c $是有限完整集的结合。后者被称为限制，具有微不足道的动态。对于特征零的非宗教自我对话，我们为典型有限的完整组的数量提供了锐利的界限。
We study the algebraic dynamics of self-correspondences on a curve. A self-correspondence on a (proper and smooth) curve $C$ over an algebraically closed field is the data of another curve $D$ and two non-constant separable morphisms $π_1$ and $π_2$ from $D$ to $C$. A subset $S$ of $C$ is complete if $π_1^{-1}(S)=π_2^{-1}(S)$. We show that self-correspondences are divided into two classes: those that have only finitely many finite complete sets, and those for which $C$ is a union of finite complete sets. The latter ones are called finitary and have a trivial dynamics. For a non-finitary self-correspondence in characteristic zero, we give a sharp bound for the number of étale finite complete sets.
