The Chabauty-Coleman bound at a prime of bad reduction
David Brown
TL;DR
This paper extends the Chabauty-Coleman bound, a key tool in number theory for estimating rational points on curves, to cases where the curve has bad reduction at a prime, broadening its applicability.
Contribution
It provides a refined bound for rational points on curves of genus greater than one with bad reduction, enhancing previous results that only applied to good reduction cases.
Findings
Extended the Chabauty-Coleman bound to bad reduction cases
Provided explicit bounds for rational points in new settings
Broadened the applicability of the Chabauty-Coleman method
Abstract
We extend the refined version of the Chabauty-Coleman bound on the number of rational points on a curve of genus g>1 to the case of bad reduction.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Polynomial and algebraic computation