On the Euler characteristic of $S$-arithmetic groups
Group Theory
2026-02-19 v3 Number Theory
Abstract
We show that the sign of the Euler characteristic of an -arithmetic subgroup of a simple algebraic group depends on the -congruence completion only, except possibly in type . Consequently, the sign is a profinite invariant for such -arithmetic groups with the congruence subgroup property. This generalizes previous work of the first author with Kionke--Raimbault--Sauer.
Cite
@article{arxiv.2405.05050,
title = {On the Euler characteristic of $S$-arithmetic groups},
author = {Holger Kammeyer and Giada Serafini},
journal= {arXiv preprint arXiv:2405.05050},
year = {2026}
}
Comments
24 pages. Extended main result. Final version to appear in J. Lond. Math. Soc