2020/08/21 by Netan Dogra, Dogra, Netan
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2008.09560
openalex publication_date 2020/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Results in p-adic transcendence theory are applied to two problems in the Chabauty-Coleman method. The first is a question of McCallum and Poonen regarding repeated roots of Coleman integrals. The second is to give lower bounds on the p-adic distance between rational points in terms of the heights of a set of Mordell-Weil generators of the Jacobian. We also explain how, in some cases, a conjecture on the 'Wieferich statistics' of Jacobians of curves implies a bound on the height of rational points of curves of small rank, in terms of the usual invariants of the curve and the height of Mordell-Weil generators of its Jacobian. The proof uses the Chabauty-Coleman method, together with effective methods in transcendence theory. We also discuss generalisations to the Chabauty-Kim method.