Congruence kernels around affine curves
Abstract
Let S be a smooth affine algebraic curve, and let S' be the Riemann surface obtained by removing a point from S. We provide evidence for the congruence subgroup property of the mapping class group Mod(S') by showing that its congruence kernel lies in the centralizer of every braid in Mod(S'). 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 for curves with at least two punctures, as well as a new proof of Matsumoto's theorem that the congruence kernel depends only on the genus in the affine case.
Cite
@article{arxiv.1109.1267,
title = {Congruence kernels around affine curves},
author = {Richard Peabody Kent},
journal= {arXiv preprint arXiv:1109.1267},
year = {2014}
}
Comments
v3. Referees' comments incorporated. Simple-connectivity statement added. To appear in Journal fur die reine und angewandte Mathematik. 23 pages, one figure. v2. A new proof of Asada's theorem that the congruence subgroup property holds in genus one has been added. Some minor changes to notation. 20 pages, one figure. v1. 18 pages, no figures