AAG Seminar - Unexpected points in quadratic Chabauty loci

Speaker: Alexander Betts, Harvard University

Abstract: TBA

Host: The Chabauty--Coleman and quadratic Chabauty methods are techniques for trying to compute the rational points on curves by finding p-adic functions which vanish on the rational points. It turns out that these functions can vanish at other, non-rational points, even in cases where a dimension heuristic predicts that this should not occur. In this talk, I will explain this phenomenon, and discuss ongoing work with Jennifer Balakrishnan in which we begin to classify these unexpected points in the case of once-punctured elliptic curves of rank 0, building on results of Francesca Bianchi.