The Valuative Section Conjecture, Étale Homotopy, and Berkovich Spaces

2023/04/08 by Jesse Pajwani, Pajwani, Jesse
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2304.03970

openalex publication_date 2023/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reinterpret a result of Pop and Stix on the p-adic section conjecture in terms of Berkovich spaces and fixed points. In doing this, we see a version of the result extends to larger classes of fields, which in turn allows us to prove a valuative section conjecture type result for a larger class of varieties. This adds to the programme to reinterpret anabelian geometry results in terms of étale homotopy types.

Related

• On the real Section Conjecture in étale homotopy theory
• On the "Section Conjecture" in anabelian geometry
• Arithmetic in the fundamental group of a p-adic curve: On the p-adic\n section conjecture for curves
• Section and towers
• Birational p-adic Galois sections in higher dimensions