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arXiv · 2410.22474

The \'etale topos reconstructs varieties over sub-p-adic fields

Magnus Carlson·Jakob Stix
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Abstract

Let $K$ be a sub-$p$-adic field. We show that the functor sending a finite type $K$-scheme to its \'etale topos is fully faithful after localizing at the class of universal homeomorphisms. This generalizes a result of Voevodsky, who proved the analogous theorem for fields finitely generated over $\mathbb{Q}$. Our proof relies on Mochizuki's Hom-theorem in anabelian geometry, and a study of point-theoretic morphisms of fundamental groups of curves.

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Magnus Carlson, Jakob Stix. 2024-10-29. The \'etale topos reconstructs varieties over sub-p-adic fields. https://arxiv.org/abs/2410.22474

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