AI 中文总结
本文在次p进域上有限型正规基概型S上，研究双曲曲线族的阿贝尔几何性质，证明其相对于优态射在光滑S概型中具有阿贝尔性，拓展了阿贝尔几何的研究范围。
AI 中文摘要
作为尝试用平展拓扑数据描述几何的阿贝尔几何，迄今主要处理域上的簇范畴。本文在次p进域上有限型的正规基概型S上研究，证明S上的双曲曲线族相对于优态射，在光滑S概型中具有阿贝尔性。
英文摘要
Anabelian geometry as an attempt to describe geometry in terms of étale topological data has addressed so far mainly categories of varieties over a field. In this paper we work over a normal base scheme $S$ of finite type over a sub-$p$-adic field and show that families of hyperbolic curves over $S$ are anabelian among smooth $S$-schemes with respect to dominant morphisms.
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