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arXiv · 2405.05050

On the Euler characteristic of $S$-arithmetic groups

Holger Kammeyer·Giada Serafini
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Abstract

We show that the sign of the Euler characteristic of an $S$-arithmetic subgroup of a simple algebraic group depends on the $S$-congruence completion only, except possibly in type ${}^6 D_4$. Consequently, the sign is a profinite invariant for such $S$-arithmetic groups with the congruence subgroup property. This generalizes previous work of the first author with Kionke--Raimbault--Sauer.

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Holger Kammeyer, Giada Serafini. 2024-05-08. On the Euler characteristic of $S$-arithmetic groups. https://arxiv.org/abs/2405.05050

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