Two recent p-adic approaches towards the (effective) Mordell conjecture
Number Theory
2020-01-22 v2 Algebraic Geometry
Abstract
We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usually called the method of Chabauty--Kim or non-abelian Chabauty in the literature, has the advantage that in some cases it has been turned into an effective method to determine the set of rational points on a curve, and we illustrate this by presenting three new examples of modular curves where this set can be determined.
Cite
@article{arxiv.1910.12755,
title = {Two recent p-adic approaches towards the (effective) Mordell conjecture},
author = {Jennifer S. Balakrishnan and Alex J. Best and Francesca Bianchi and Brian Lawrence and J. Steffen Müller and Nicholas Triantafillou and Jan Vonk},
journal= {arXiv preprint arXiv:1910.12755},
year = {2020}
}
Comments
Corrected Theorem 6.3 and its proof. Added short discussion of non-proper hyperbolic curves