\(S\)-arithmetic spinor groups with the same finite quotients and distinct \(\ell^2\)-cohomology (Q2032439)
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scientific article; zbMATH DE number 7357936
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(S\)-arithmetic spinor groups with the same finite quotients and distinct \(\ell^2\)-cohomology |
scientific article; zbMATH DE number 7357936 |
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\(S\)-arithmetic spinor groups with the same finite quotients and distinct \(\ell^2\)-cohomology (English)
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11 June 2021
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Summary: 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 \(i\geq 2\).
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\(\ell^2\)-Betti numbers
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profinite completion
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\(S\)-arithmetic groups
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