Families of curves separating points

2026/07/30 by Wojciech Porowski
Mathematics · #math.AG #msc:14H30 #msc:14F35 #msc:14D99

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arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We show that for a hyperbolic curve X over an algebraically closed field k of characteristic zero and a finite set S of k-rational points of X, after replacing X by a finite étale cover, there exists a family of curves over X whose fibres over points in S have pairwise nonisogenous Jacobians. We also give an application of our results to a problem concerning Galois sections.

Citations

• Locally conjugate Galois sections
• Galois sections and p-adic period mappings
• Diophantine problems and p-adic period mappings
• Coverings in p-adic analytic geometry and log coverings I: Cospecialization of the (p')-tempered fundamental group for a family of curves
• A monodromy criterion for extending curves

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