On reductions of Selmer sections

2025/09/19 by Wojciech Porowski, Porowski, Wojciech
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2509.15660

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

Abstract

We consider reductions of Selmer sections of the étale homotopy sequence of a hyperbolic curve over a number field. We show that the conjugacy class of a noncuspidal Selmer section is uniquely determined by its reduction on a set of density one. Moreover, we show that a noncuspidal Selmer section reduces to cusps only on a set of density zero, at least after a finite field extension.

Citations

• Locally conjugate Galois sections
• Galois sections and p-adic period mappings
• On cuspidal sections of algebraic fundamental groups
• A monodromy criterion for extending curves
• The density of ramified primes in semisimple p-adic Galois representations

Related

• Locally conjugate Galois sections
• Galois sections and p-adic period mappings
• On the section conjecture over fields of finite type
• On cuspidal sections of algebraic fundamental groups
• A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves