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arXiv · 2509.23485

\'Etale Reconstruction for $\mathbb{F}_p(t)$-Schemes

Zachary Berens
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Abstract

Voevodsky proved that normal schemes of finite type over finitely generated fields of characteristic $0$ can be reconstructed from their \'etale sites. Let $K$ be a field that is finitely generated over $\mathbb{F}_p(t)$. Grothendieck conjectured that perfections of finite type $K$-schemes can be reconstructed from their \'etale sites. Adapting Voevodsky's methods, we prove this.

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Zachary Berens. 2025-09-27. \'Etale Reconstruction for $\mathbb{F}_p(t)$-Schemes. https://arxiv.org/abs/2509.23485

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