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Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi +4
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 usual…
Archimedean local height differences on elliptic curves
J. Steffen Müller, Corinna Stumpe
To compute generators for the Mordell-Weil group of an elliptic curve over a number field, one needs to bound the difference between the naive and the canonical height from above.…
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller +2
We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compu…
A height inequality for rational points on elliptic curves implied by the abc-conjecture
Ulf Kühn, J. Steffen Müller
In this short note we show that the uniform abc-conjecture over number fields puts strong restrictions on the coordinates of rational points on elliptic curves. For the proof we us…