A refined Chabauty--Coleman bound for surfaces

2025/01/07 by Balakrishnan, Jennifer S., Caro, Jerson
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.03483

Abstract

Caro and Pasten gave an explicit upper bound on the number of rational points on a hyperbolic surface that is embedded in an abelian variety of rank at most one. We show how to use their method to produce a refined bound on the number of rational points on the surface W₂ := C+C in the case of a hyperelliptic curve C of genus 3 over ℚ. Combining this with work of Siksek, we use this to determine W₂(ℚ) in a selection of examples.

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