Linear and quadratic Chabauty for affine hyperbolic curves
arXiv:2301.11193 · doi:10.1093/imrn/rnad185
Abstract
We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth quotients of the fundamental group, following a construction of Balakrishnan-Dogra in the projective case. We also apply Betts' machinery of weight filtrations to give unconditional explicit upper bounds on the number of S-integral points when our conditions are satisfied.
20 pages; comments welcome