Refined Chabauty–Kim for the thrice-punctured lineMPIM

Wednesday Apr 23, 2025, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

If X is a curve of genus at least two defined over the rational numbers, we know by Faltings's Theorem that the set X(Q) of rational points is finite, but how to systematically compute it is still an open problem. In 2005, Minhyong Kim proposed a new framework for studying rational (or S-integral) points on curves, called Chabauty–Kim theory. It aims to produce p-adic analytic functions on X(Q_p) containing the rational points X(Q) in their zero locus. I will give a brief introduction to Chabauty–Kim theory and present some applications to the S-unit equation.