Abstract
Let \(\mathbf {G}\) 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. The congruence subgroup kernel measures what proportion of S-arithmetic subgroups of \(\mathbf {G}\) are S-congruence subgroups. In this paper, a topological realization of the congruence subgroup kernel is given using the locally symmetric spaces associated with G and its S-arithmetic subgroups. The construction uses the reductive Borel–Serre compactifications of these spaces. The congruence subgroup kernel then appears as a fundamental group.
To Kumar Murty on his 60th birthday
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Scherk, J. (2018). A Topological Realization of the Congruence Subgroup Kernel. In: Akbary, A., Gun, S. (eds) Geometry, Algebra, Number Theory, and Their Information Technology Applications. GANITA 2016. Springer Proceedings in Mathematics & Statistics, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-319-97379-1_18
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DOI: https://doi.org/10.1007/978-3-319-97379-1_18
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