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Flatmates and the bounded cohomology of algebraic groups (2407.01709v2)
Published 1 Jul 2024 in math.GR, math.AG, and math.AT
Abstract: For all algebraic groups over non-Archimedean local fields, the bounded cohomology vanishes. This follows from the corresponding statement for automorphism groups of Bruhat--Tits buildings, which hinges on the solution to the flatmate conjecture raised in earlier work with Bucher. Vanishing and invariance theorems for arithmetic groups are derived.
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