Étale Reconstruction for \mathbbF_p(t)-Schemes

2025/09/27 by Zachary Berens, Berens, Zachary
Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2509.23485

openalex publication_date 2025/09/27 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

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

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• Reconstruction of schemes from their étale topoi
• The étale topos reconstructs varieties over sub-p-adic fields
• Topological reconstruction theorems over uncountable algebraically closed fields
• An étale realization which does not exist
• A reconstruction theorem for varieties