Congruence kernels around affine curves

Let S be a smooth affine algebraic curve, and let S̊ be the Riemann surface obtained by removing a point from S. We provide evidence for the congruence subgroup property of mapping class groups by showing that the congruence kernel ker ( M̂od(S̊)→ Out ( π̂1(S̊) )) lies in the centralizer of every braid in Mod(S̊). As a corollary, we obtain a new proof of Asada’s theorem that the congruence subgroup property holds in genus one. We also obtain simple–connectivity of Boggi’s procongruence curve complex Č (S̊) when S is affine, and a new proof of Matsumoto’s theorem that the congruence kernel depends only on the genus in the affine case.