Curves with sharp Chabauty-Coleman bound

2020/09/02 by Gajović, Stevan · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2009.01084

Abstract

We construct curves of each genus g≥ 2 for which Coleman's effective Chabauty bound is sharp and Coleman's theorem can be applied to determine rational points if the rank condition is satisfied. We give numerous examples of genus two and rank one curves for which Coleman's bound is sharp. Based on one of those curves, we construct an example of a curve of genus five whose rational points are determined using the descent method together with Coleman's theorem.

Cited by

• Infinitely many genus two and three curves of small fixed positive rank

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