The method of Chabauty and Coleman. (English. French summary) Zbl 1377.11077

Belabas, Karim et al., Explicit methods in number theory. Rational points and Diophantine equations. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-359-1/pbk). Panoramas et Synthèses 36, 99-117 (2012).
Summary: This is an introduction to the method of Chabauty and Coleman, a \(p\)-adic method that attempts to determine the set of rational points on a given curve of genus \(g\geq 2\). We present the method, give a few examples of its implementation in practice, and discuss its effectiveness. An appendix treats the case in which the curve has bad reduction.
For the entire collection see [Zbl 1267.11002].


11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
14G05 Rational points
14K20 Analytic theory of abelian varieties; abelian integrals and differentials