Math @ Duke
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Publications [#226574] of Leslie Saper
Papers Published
- 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.
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