Math @ Duke

Publications [#192270] of Leslie D. Saper
Papers Submitted
 L. Ji, K. Murty, L. Saper, and J. Scherk, The Congruence Subgroup Kernel and the Fundamental Group of the Reductive BorelSerre 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 BruhatTits
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 BorelSerre compactification of Γ \ X for
certain sufficiently small Sarithmetic subgroups Γ of G. Our
result follows from explicit computations of the fundamental group of the
reductive BorelSerre 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 ksubgroups. Similar
computations of the fundamental group of the Satake
compactifications are made.


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