Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#226574] of Leslie Saper

Papers Published

  1. L. Ji, K. Murty, L. Saper, and J. Scherk, The Fundamental Group of Reductive Borel-Serre and Satake Compactifications, The Asian Journal of Mathematics, vol. 19 no. 3 (2015), pp. 465-486 [arXiv:1106.4810], [available here]
    (last updated on 2015/12/22)

    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(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 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. 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.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320