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Effective Chabauty and the Cursed Curve

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Effective Chabauty and the Cursed Curve

The Chabauty method often allows one to find the rational points on curves of genus at least 2 over the rationals, but has a lot of limitations. On a theoretical level, the Mordell-Weil rank of the Jacobian of the curve has to be strictly smaller than its genus. In practice, even when this condition is satisfied, the relevant Coleman integrals can usually only be computed for hyperelliptic curves. We will report on recent work of ours (with different combinations of collaborators) on extending the method to more general curves. In particular, we will show how one can use an extension of the Chabauty method by Kim to find the rational points on the split Cartan modular curve of level 13, which is also known as the cursed curve. The talk will be aimed at non-specialists with an interest in number theory.

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Jan Tuitman
Date : 19 janvier 2018
Horaire : 14h15 - 14h15
Lieu : Institut Henri Poincaré amphi Hermite