Publications [#192270] of Leslie D. Saper

Papers Submitted

1. L. Ji, K. Murty, L. Saper, and J. Scherk, The Congruence Subgroup Kernel and the Fundamental Group of the Reductive Borel-Serre Compactification (June, 2011) [arXiv:1106.4810]
   (last updated on 2011/12/12)

   Abstract:
   Let G be an almost simple, simply connected algebraic group defined over a number field k, and let S be a finite set of places of k including all infinite places. Let X be the product over v ∈ S of the symmetric spaces associated to G(k_v), when v is an infinite place, and the Bruhat-Tits buildings associated to G(k_v), when v is a finite place. The main result of this paper is to identify the congruence subgroup kernel with the fundamental group of the reductive Borel-Serre compactification of Γ \ X for certain sufficiently small S-arithmetic subgroups Γ of G. Our result follows from explicit computations of the fundamental group of the reductive Borel-Serre compactifications of Γ \ X. In the case that Γ is neat, we show that this fundamental group is isomorphic to Γ / EΓ, where EΓ is the subgroup generated by the elements of Γ belonging to unipotent radicals of parabolic k-subgroups. Similar computations of the fundamental group of the Satake compactifications are made.