Anabelian Geometry in Families

Tim Holzschuh; Alexander Schmidt; Jakob Stix

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arXiv · 2608.21232

Anabelian Geometry in Families

Tim Holzschuh·Alexander Schmidt·Jakob Stix

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Abstract

Anabelian geometry as an attempt to describe geometry in terms of \'etale 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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Tim Holzschuh, Alexander Schmidt, Jakob Stix. 2026-08-21. Anabelian Geometry in Families. https://arxiv.org/abs/2608.21232

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