论文标题
高度和算术动力学在有限生成的字段上
Heights and arithmetic dynamics over finitely generated fields
论文作者
论文摘要
我们开发了相对于有限生成的扩展K/K的矢量值高度和交叉点的理论。这些概括了数字字段和几何高度。当k是Q或f_p，或者当非丧失性条件保持时，我们将获得Northcott-Type结果。然后，我们证明了用于矢量值相交的Hodge索引定理的一个版本，并使用它证明了任何字段上极性动力学系统的刚度定理。
We develop a theory of vector-valued heights and intersections defined relative to finitely generated extensions K/k. These generalize both number field and geometric heights. When k is Q or F_p, or when a non-isotriviality condition holds, we obtain Northcott-type results. We then prove a version of the Hodge Index Theorem for vector-valued intersections, and use it to prove a rigidity theorem for polarized dynamical systems over any field.
