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Two recent p-adic approaches towards the (effective) Mordell conjecture

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arxiv 1910.12755 v2 pith:XS4B4JA4 submitted 2019-10-28 math.NT math.AG

Two recent p-adic approaches towards the (effective) Mordell conjecture

Jennifer S. Balakrishnan , Alex J. Best , Francesca Bianchi , Brian Lawrence , J. Steffen M\"uller , Nicholas Triantafillou , Jan Vonk This is my paper
classification math.NT math.AG
keywords effectivemethodapproachesconjecturemordellrecenttowardsaccount
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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.

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