The fundamental group of reductive Borel–Serre and Satake compactifications

Published

Journal Article

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 ε S of the symmetric spaces associated to G(kv), when v is an infinite place, and the Bruhat-Tits buildings associated to G(kv), when v is a finite place. The main result of this paper is to compute explicitly the fundamental group of the reductive Borel-Serre compactification of Γ\X, where Γ is an S-arithmetic subgroup of G. In the case that G 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 k-parabolic subgroups. Analogous computations of the fundamental group of the Satake compactifications are made. It is noteworthy that calculations of the congruence subgroup kernel C(S, G) yield similar results.

Full Text

Duke Authors

Cited Authors

  • Ji, L; Murty, VK; Saper, L; Scherk, J

Published Date

  • 2015

Published In

Volume / Issue

  • 19 / 3

Start / End Page

  • 465 - 486

Electronic International Standard Serial Number (EISSN)

  • 1945-0036

International Standard Serial Number (ISSN)

  • 1093-6106

Digital Object Identifier (DOI)

  • 10.4310/AJM.2015.v19.n3.a4