Math @ Duke

Publications [#320536] of Leslie Saper
Papers Published
 Ji, L; Murty, VK; Saper, L; Scherk, J, The fundamental group of reductive Borel–Serre and Satake compactifications,
Asian Journal of Mathematics, vol. 19 no. 3
(2015),
pp. 465486 [arXiv:1106.4810], [available here], [doi]
(last updated on 2018/04/20)
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 ε S of the symmetric spaces associated to G(kv), when v is an infinite place, and the BruhatTits 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 BorelSerre compactification of Γ\X, where Γ is an Sarithmetic 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 kparabolic 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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