Let $C$ be a curve over the rationals of genus $g \geq 2$. Such a curve has finitely many rational points, but finding them all is difficult. Assuming the rank of the Mordell-Weil group of the Jacobian is less than $g$, the Chabauty-Coleman method is very effective in practice, returning a small set of $p$-adic points containing the set of rational points. In this talk I will discuss a variant of Chabauty, geometric linear Chabauty (based on geometric quadratic Chabauty as developed by Edixhoven and Lido), that can outperform Chabauty-Coleman in some cases; I will compare this method to the classical Chabauty-Coleman method, and characterise the differences. If time permits, I will also talk about ongoing work in (geometric) quadratic Chabauty, an extension of Chabauty's method. This talk is based on joint work with Sachi Hashimoto and Juanita Duque-Rosero.
Freitag, den 24. Juni 2022 um 13:30 Uhr, in INF 205, SR A Freitag, den 24. Juni 2022 at 13:30, in INF 205, SR A
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Marius Leonhardt