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A Robust Implementation for Solving the S-Unit Equation and Several Applications Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Curves with Sharp Chabauty-Coleman Bound

Author : Stevan Gajović

Published in: Arithmetic Geometry, Number Theory, and Computation

Publisher: Springer International Publishing

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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.

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previous chapter Computing Rational Points on Rank 0 Genus 3 Hyperelliptic Curves
next chapter Chabauty–Coleman Computations on Rank 1 Picard Curves
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Metadata
Title
Curves with Sharp Chabauty-Coleman Bound
Author
Stevan Gajović
Copyright Year
2021
Book
Arithmetic Geometry, Number Theory, and Computation

Print ISBN: 978-3-030-80913-3

Electronic ISBN: 978-3-030-80914-0

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-80914-0_15

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