GEOMETRIC QUADRATIC CHABAUTY

Determining all rational points on a curve of genus at least 2 can be difficult. Chabauty's method (1941) is to intersect, for prime number p, in the p-adic Lie group jacobian, closure Mordell-Weil with curve. If rank less than then this has never failed. Minhyong Kim's non-abelian Chabauty programme aims remove condition rank. The simplest case, called quadratic Chabauty, was developed by Balakrishnan, Dogra, Mueller, Tuitman and Vonk, applied tour de force so-called cursed (rank both 3). This article make small geometric again, describing it terms only `simple algebraic geometry' (line bundles over jacobian models integers).