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$S$-arithmetic spinor groups with the same finite quotients and distinct $\ell^2$-cohomology
Groups, Geometry, and Dynamics ( IF 0.6 ) Pub Date : 2020-10-12 , DOI: 10.4171/ggd/566
Holger Kammeyer 1 , Roman Sauer 1
Affiliation  

In this note we refine examples by Aka from arithmetic to $S$-arithmetic groups to show that the vanishing of the $i$-th $\ell^2$-Betti number is not a profinite invariant for all $i \geq 2$.

中文翻译:

具有相同有限商和不同\\ ell ^ 2 $-同调性的$ S $-算术旋转子群

在本说明中,我们将Aka的示例从算术组简化为$ S $算术组,以表明第i个$ i $ ell * 2 $ -Betti数的消失并不是所有$ i \ geq 2的无限不变$。
更新日期:2020-10-30
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