Martin Lüdtke (MPIM Bonn)

Abstract: If X is a curve of genus at least 2 defined over the rational numbers, we know by Faltings’s Theorem that the set X(Q) of rational points is finite but we don’t know how to systematically compute this set. In 2005, Minhyong Kim proposed a new framework for studying rational (or S-integral) points on curves, called the Chabauty–Kim method. It aims to produce p-adic analytic functions on X(Q_p) containing the rational points X(Q) in their zero locus. We apply this method to solve the S-unit equation for S={2,3} and computationally verify Kim’s Conjecture for many choices of the auxiliary prime p.